From 843819a3658097fc8a14d5c3aa2956b011b6d90f Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Thu, 28 May 2026 14:20:39 -0600
Subject: [PATCH 01/18] Make limit quotient tables html only

---
 project.ptx                                   |  6 +--
 ptx/sec_limit_intro.ptx                       | 18 ++++-----
 publication/publication-accelerated-web.ptx   | 40 +++++++++++++++++++
 .../publication-proteus-playground.ptx        |  2 +-
 publication/publication-runestone-proteus.ptx |  2 +-
 publication/publication-runestone.ptx         |  2 +-
 publication/publication-standard-web.ptx      | 40 +++++++++++++++++++
 publication/publication-video.ptx             |  2 +-
 publication/publication-web-novid.ptx         | 39 ++++++++++++++++++
 9 files changed, 135 insertions(+), 16 deletions(-)
 create mode 100644 publication/publication-accelerated-web.ptx
 create mode 100644 publication/publication-standard-web.ptx
 create mode 100644 publication/publication-web-novid.ptx

diff --git a/project.ptx b/project.ptx
index 8b314836b..3d701c584 100644
--- a/project.ptx
+++ b/project.ptx
@@ -4,13 +4,13 @@
     <target name="html" format="html" source="apex.ptx" publication="publication-video.ptx">
       <stringparams key="html.annotation" value="hypothesis"/>
     </target>
-    <target name="html-novideo" format="html" source="apex.ptx" publication="publication-novid.ptx">
+    <target name="html-novideo" format="html" source="apex.ptx" publication="publication-web-novid.ptx">
       <stringparams key="html.annotation" value="hypothesis"/>
     </target>
-    <target name="html-standard" format="html" source="apex-UL-standard.ptx" publication="publication-standard.ptx">
+    <target name="html-standard" format="html" source="apex-UL-standard.ptx" publication="publication-standard-web.ptx">
       <stringparams key="html.annotation" value="hypothesis"/>
     </target>
-    <target name="html-accelerated" format="html" source="apex-UL-accelerated.ptx" publication="publication-accelerated.ptx">
+    <target name="html-accelerated" format="html" source="apex-UL-accelerated.ptx" publication="publication-accelerated-web.ptx">
       <stringparams key="html.annotation" value="hypothesis"/>
     </target>
     <target name="runestone" format="html" source="apex.ptx" publication="publication-runestone.ptx" output-dir="../published/APEX">
diff --git a/ptx/sec_limit_intro.ptx b/ptx/sec_limit_intro.ptx
index 506083ae9..6be1db13a 100644
--- a/ptx/sec_limit_intro.ptx
+++ b/ptx/sec_limit_intro.ptx
@@ -1096,7 +1096,7 @@
           </sidebyside>
         </figure>
 
-        <figure xml:id="table_nolimit3c" vshift="3">
+        <figure xml:id="table_nolimit3c" vshift="2">
           <caption>Observing that <m>f(x)=\sin(1/x)</m> has no limit as <m>x\to0</m> in <xref ref="ex_no_limit3"/></caption>
           <tabular>
             <row bottom="medium">
@@ -3484,7 +3484,7 @@
                 <m>f(x)=<var name="$f"/></m>,
                 <m>a=<var name="$a"/></m>
               </p>
-              <tabular top="major">
+              <tabular top="major" component="web">
                 <col halign="center"/>
                 <col halign="center"/>
                 <row bottom="medium">
@@ -3604,7 +3604,7 @@
                 <m>f(x)=<var name="$f"/></m>,
                 <m>a=<var name="$a"/></m>
               </p>
-              <tabular top="major">
+              <tabular top="major" component="web">
                 <col halign="center"/>
                 <col halign="center"/>
                 <row bottom="medium">
@@ -3727,7 +3727,7 @@
                 <m>f(x)=<var name="$f"/></m>,
                 <m>a=<var name="$a"/></m>
               </p>
-              <tabular top="major">
+              <tabular top="major" component="web">
                 <col halign="center"/>
                 <col halign="center"/>
                 <row bottom="medium">
@@ -3848,7 +3848,7 @@
                 <m>f(x)=<var name="$f"/></m>,
                 <m>a=<var name="$a"/></m>
               </p>
-              <tabular top="major">
+              <tabular top="major" component="web">
                 <col halign="center"/>
                 <col halign="center"/>
                 <row bottom="medium">
@@ -3975,7 +3975,7 @@
                 <m>f(x)=<var name="$f"/></m>,
                 <m>a=<var name="$a"/></m>
               </p>
-              <tabular top="major">
+              <tabular top="major" component="web">
                 <col halign="center"/>
                 <col halign="center"/>
                 <row bottom="medium">
@@ -4092,7 +4092,7 @@
                 <m>f(x)=<var name="$f"/></m>,
                 <m>a=<var name="$a"/></m>
               </p>
-              <tabular top="major">
+              <tabular top="major" component="web">
                 <col halign="center"/>
                 <col halign="center"/>
                 <row bottom="medium">
@@ -4210,7 +4210,7 @@
                 <m>f(x)=<var name="$f"/></m>,
                 <m>a=<var name="$a"/></m>
               </p>
-              <tabular top="major">
+              <tabular top="major" component="web">
                 <col halign="center"/>
                 <col halign="center"/>
                 <row bottom="medium">
@@ -4328,7 +4328,7 @@
                 <m>f(x)=<var name="$f"/></m>,
                 <m>a=<var name="$a"/></m>
               </p>
-              <tabular top="major">
+              <tabular top="major" component="web">
                 <col halign="center"/>
                 <col halign="center"/>
                 <row bottom="medium">
diff --git a/publication/publication-accelerated-web.ptx b/publication/publication-accelerated-web.ptx
new file mode 100644
index 000000000..111b3f6fb
--- /dev/null
+++ b/publication/publication-accelerated-web.ptx
@@ -0,0 +1,40 @@
+<?xml version="1.0" encoding="UTF-8"?>
+
+<publication>
+
+    <!-- Relative path, relative to "main" source file -->
+    <source>
+        <directories external="../assets" generated="../generated-assets-accelerated"/>
+        <version include="main color video taypoly-early video-early web"/>
+    </source>
+
+    <webwork server="https://webwork-dev.uleth.ca" course="apex-accelerated"/>
+
+    <common>
+      <tableofcontents level="3"/>
+      <exercise-divisional hint="no" answer="no" solution="no"/>
+      <exercise-reading hint="yes" answer="no" solution="no"/>
+    </common>
+    <!-- HTML-Specific Options -->
+    <html>
+        <calculator model="geogebra-graphing"/>
+        <index-page ref="apex-calculus"/>
+        <video privacy="yes"/>
+        <!-- baseurl should not have a trailing slash -->
+        <baseurl href="https://opentext.uleth.ca/apex-accelerated"/>
+        <knowl example="no"/>
+        <asymptote links="yes"/>
+        <webwork divisional="dynamic" reading="dynamic"/>
+        <!-- <css toc="crc" banner="crc" navbar="crc" shell="crc"/> -->
+    </html>
+    <!-- PDF-Specific Options -->
+    <latex print="no" sides="one">
+      <asymptote links="yes"/>
+      <page>
+        <geometry>inner=1in,textheight=9in,textwidth=320pt,marginparwidth=150pt,marginparsep=20pt,bottom=1in,footskip=29pt</geometry>
+      </page>
+    </latex>
+    <epub>
+      <cover front="cover/cover.png"/>
+    </epub>
+</publication>
diff --git a/publication/publication-proteus-playground.ptx b/publication/publication-proteus-playground.ptx
index 7d542ae5f..203bf03c5 100644
--- a/publication/publication-proteus-playground.ptx
+++ b/publication/publication-proteus-playground.ptx
@@ -5,7 +5,7 @@
     <!-- Relative path, relative to "main" source file -->
     <source>
         <directories external="../assets" generated="../generated-assets-playground"/>
-        <version include="playground-id proteus playground color video taypoly-late video-late"/>
+        <version include="playground-id proteus playground color video taypoly-late video-late web"/>
     </source>
 
     <webwork server="https://webwork-dev.uleth.ca" course="apex-main"/>
diff --git a/publication/publication-runestone-proteus.ptx b/publication/publication-runestone-proteus.ptx
index b54e4a9c7..dbbab0bd7 100644
--- a/publication/publication-runestone-proteus.ptx
+++ b/publication/publication-runestone-proteus.ptx
@@ -5,7 +5,7 @@
     <!-- Relative path, relative to "main" source file -->
     <source>
         <directories external="../assets" generated="../generated-assets-proteus"/>
-        <version include="proteus-id proteus color video taypoly-late video-late"/>
+        <version include="proteus-id proteus color video taypoly-late video-late web"/>
     </source>
 
     <webwork server="https://webwork-dev.uleth.ca" course="apex-main"/>
diff --git a/publication/publication-runestone.ptx b/publication/publication-runestone.ptx
index 0de9f25b4..5bb157db3 100644
--- a/publication/publication-runestone.ptx
+++ b/publication/publication-runestone.ptx
@@ -5,7 +5,7 @@
     <!-- Relative path, relative to "main" source file -->
     <source>
         <directories external="../assets" generated="../generated-assets"/>
-        <version include="main color video taypoly-late video-late"/>
+        <version include="main color video taypoly-late video-late web"/>
     </source>
 
     <webwork server="https://webwork-dev.uleth.ca" course="apex-main"/>
diff --git a/publication/publication-standard-web.ptx b/publication/publication-standard-web.ptx
new file mode 100644
index 000000000..eb5c1a513
--- /dev/null
+++ b/publication/publication-standard-web.ptx
@@ -0,0 +1,40 @@
+<?xml version="1.0" encoding="UTF-8"?>
+
+<publication>
+
+    <!-- Relative path, relative to "main" source file -->
+    <source>
+        <directories external="../assets" generated="../generated-assets-standard"/>
+        <version include="main color video taypoly-early video-early web"/>
+    </source>
+
+    <webwork server="https://webwork-dev.uleth.ca" course="apex-standard"/>
+
+    <common>
+      <tableofcontents level="3"/>
+      <exercise-divisional hint="no" answer="no" solution="no"/>
+      <exercise-reading hint="yes" answer="no" solution="no"/>
+    </common>
+    <!-- HTML-Specific Options -->
+    <html>
+        <calculator model="geogebra-graphing"/>
+        <index-page ref="apex-calculus"/>
+        <video privacy="yes"/>
+        <!-- baseurl should not have a trailing slash -->
+        <baseurl href="https://opentext.uleth.ca/apex-standard"/>
+        <knowl example="no"/>
+        <asymptote links="yes"/>
+        <webwork divisional="dynamic" reading="dynamic"/>
+        <!-- <css toc="crc" banner="crc" navbar="crc" shell="crc"/> -->
+    </html>
+    <!-- PDF-Specific Options -->
+    <latex print="no" sides="one">
+      <asymptote links="yes"/>
+      <page>
+        <geometry>inner=1in,textheight=9in,textwidth=320pt,marginparwidth=150pt,marginparsep=20pt,bottom=1in,footskip=29pt</geometry>
+      </page>
+    </latex>
+    <epub>
+      <cover front="cover/cover.png"/>
+    </epub>
+</publication>
diff --git a/publication/publication-video.ptx b/publication/publication-video.ptx
index 68c2b5c6f..35fe35b32 100644
--- a/publication/publication-video.ptx
+++ b/publication/publication-video.ptx
@@ -5,7 +5,7 @@
     <!-- Relative path, relative to "main" source file -->
     <source>
         <directories external="../assets" generated="../generated-assets-video"/>
-        <version include="main color video taypoly-late video-late"/>
+        <version include="main color video taypoly-late video-late web"/>
     </source>
 
     <webwork server="https://webwork-dev.uleth.ca" course="apex-video"/>
diff --git a/publication/publication-web-novid.ptx b/publication/publication-web-novid.ptx
new file mode 100644
index 000000000..4dd96d3f1
--- /dev/null
+++ b/publication/publication-web-novid.ptx
@@ -0,0 +1,39 @@
+<?xml version="1.0" encoding="UTF-8"?>
+
+<publication>
+
+    <!-- Relative path, relative to "main" source file -->
+    <source>
+        <directories external="../assets" generated="../generated-assets"/>
+        <version include="main color novideo taypoly-late web"/>
+    </source>
+
+    <webwork server="https://webwork-dev.uleth.ca" course="apex-main"/>
+
+    <common>
+      <tableofcontents level="2"/>
+      <exercise-divisional hint="no" answer="no" solution="no"/>
+      <exercise-reading hint="yes" answer="no" solution="no"/>
+    </common>
+    <!-- HTML-Specific Options -->
+    <html>
+        <calculator model="geogebra-graphing"/>
+        <index-page ref="apex-calculus"/>
+        <video privacy="yes"/>
+        <!-- baseurl should not have a trailing slash -->
+        <baseurl href="https://opentext.uleth.ca/apex-calculus"/>
+        <knowl example="no"/>
+        <asymptote links="yes"/>
+        <webwork divisional="dynamic"/>
+    </html>
+    <!-- PDF-Specific Options -->
+    <latex print="no" sides="one">
+      <asymptote links="yes"/>
+      <page>
+        <geometry>inner=1in,textheight=9in,textwidth=320pt,marginparwidth=150pt,marginparsep=20pt,bottom=1in,footskip=29pt</geometry>
+      </page>
+    </latex>
+    <epub>
+      <cover front="cover/cover.png"/>
+    </epub>
+</publication>

From 548ad256ef6b112daf47e5678d069b33579f3bb0 Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Tue, 2 Jun 2026 16:14:47 -0600
Subject: [PATCH 02/18] adjust margin figure alignment

---
 ptx/sec_ABC.ptx                  |    4 +-
 ptx/sec_Graphical_Numerical.ptx  |   19 +-
 ptx/sec_Separable.ptx            |    2 +-
 ptx/sec_alt_series.ptx           |    2 +-
 ptx/sec_arc_length.ptx           |    4 +-
 ptx/sec_center_of_mass.ptx       |    2 +-
 ptx/sec_conic_sections.ptx       |    4 +-
 ptx/sec_def_int.ptx              |    4 +-
 ptx/sec_double_int_volume.ptx    |    8 +-
 ptx/sec_fluid_force.ptx          |    2 +-
 ptx/sec_graph_extreme_values.ptx |   14 +-
 ptx/sec_greensthm.ptx            |    4 +-
 ptx/sec_int_comp_tests.ptx       |  151 ++--
 ptx/sec_lhopitals_rule.ptx       |    2 +-
 ptx/sec_limit_analytically.ptx   |    2 +-
 ptx/sec_limit_continuity.ptx     |   22 +-
 ptx/sec_limit_def.ptx            |    6 +-
 ptx/sec_limit_onesided.ptx       |    4 +-
 ptx/sec_lines.ptx                |    2 +-
 ptx/sec_multi_extreme_values.ptx |    2 +-
 ptx/sec_multi_tangent.ptx        |    6 +-
 ptx/sec_par_calc.ptx             |    4 +-
 ptx/sec_polar.ptx                | 1108 +++++++++++++++---------------
 ptx/sec_sequences.ptx            |   12 +-
 ptx/sec_series.ptx               |   10 +-
 ptx/sec_space_coord.ptx          |    4 +-
 ptx/sec_vector_intro.ptx         |   10 +-
 ptx/sec_vvf_calc.ptx             |    2 +-
 ptx/sec_vvf_motion.ptx           |    2 +-
 29 files changed, 711 insertions(+), 707 deletions(-)

diff --git a/ptx/sec_ABC.ptx b/ptx/sec_ABC.ptx
index 598d80bfd..8368145e4 100644
--- a/ptx/sec_ABC.ptx
+++ b/ptx/sec_ABC.ptx
@@ -245,7 +245,7 @@
         as shown in <xref ref="fig_abc1"/>.
       </p>
 
-      <figure xml:id="fig_abc1" vshift="3">
+      <figure xml:id="fig_abc1" vshift="2">
         <caption>Graphing an enclosed region in <xref ref="ex_abc1"/></caption>
         <!-- START figures/fig_abc1.tex -->
         <image width="47%">
@@ -403,7 +403,7 @@
         <m>y=-(x-1)^2+3</m> and <m>y=2</m>,
         as shown in <xref ref="fig_abc3"/>.
       </p>
-      <figure xml:id="fig_abc3" vshift="0">
+      <figure xml:id="fig_abc3" vshift="-1">
         <caption>Graphing a region for <xref ref="ex_abc3"/></caption>
         <!-- START figures/fig_abc3.tex -->
         <image width="47%">
diff --git a/ptx/sec_Graphical_Numerical.ptx b/ptx/sec_Graphical_Numerical.ptx
index ba415a278..9c6f6eb02 100644
--- a/ptx/sec_Graphical_Numerical.ptx
+++ b/ptx/sec_Graphical_Numerical.ptx
@@ -1383,6 +1383,7 @@
     <p>
       Let's practice Euler's Method using a few concrete examples.
     </p>
+
     <example xml:id="ex_euler1">
       <title>Using Euler's Method 1</title>
       <statement>
@@ -1407,13 +1408,9 @@
           </md>.
         </p>
         <p>
-          Using Euler's method, we find the approximate <m>y(2) \approx -0.75</m>.
-        </p>
-        <p>
-          To help visualize the Euler's method approximation, these three points
-          (connected by line segments)
-          are plotted along with the analytical solution to the initial value problem in <xref ref="fig_20_01_euler1"/>.
+          Using Euler's method, we find the approximation <m>y(2) \approx -0.75</m>.
         </p>
+
         <figure xml:id="fig_20_01_euler1" vshift="2">
           <caption>Euler's Method approximation to <m>\yp = x + y</m> with <m>y(1) = -1</m> from <xref ref="ex_euler1"/>,
           along with the analytical solution to the initial value problem</caption>
@@ -1452,6 +1449,12 @@
             </latex-image>
           </image>
         </figure>
+
+        <p>
+          To help visualize the Euler's method approximation, these three points
+          (connected by line segments)
+          are plotted along with the analytical solution to the initial value problem in <xref ref="fig_20_01_euler1"/>.
+        </p>
       </solution>
     </example>
 
@@ -1498,7 +1501,7 @@
           along with the points from <xref ref="ex_euler1"/> and the analytic solution,
           are plotted in <xref ref="fig_20_01_euler2"/>.
         </p>
-        <figure xml:id="fig_20_01_euler2" vshift="0">
+        <figure xml:id="fig_20_01_euler2" vshift="3">
           <caption>Euler's Method approximations to <m>\yp = x + y</m> with <m>y(1) = -1</m> from <xref ref="ex_euler1" text="global">Examples</xref>
             and <xref ref="ex_euler2" text="global"/>, along with the analytical solution</caption>
           <image width="47%">
@@ -1642,7 +1645,7 @@
           are plotted in <xref ref="fig_20_01_euler3"/>.
           Notice how well they seem to match the true solution.
         </p>
-        <figure xml:id="fig_20_01_euler3" vshift="2">
+        <figure xml:id="fig_20_01_euler3" vshift="3">
           <caption>Euler's Method approximation to <m>\yp = y(1-y)</m> with <m>y(0) = 0.25</m> from <xref ref="ex_euler3"/>,
           along with the analytical solution</caption>
           <image width="47%">
diff --git a/ptx/sec_Separable.ptx b/ptx/sec_Separable.ptx
index bb6010b98..8ca6b966c 100644
--- a/ptx/sec_Separable.ptx
+++ b/ptx/sec_Separable.ptx
@@ -507,7 +507,7 @@
       </solution>
     </example>
 
-    <aside vshift="-1">
+    <aside vshift="1">
       <p>
         Solving for <m>y</m> initially yields the explicit solution <m>\displaystyle y = \frac{AMe^{kt}}{1+Ae^{kt}}</m>.
         Dividing numerator and denominator by <m>Ae^{kt}</m> and defining <m>b = 1/A</m>
diff --git a/ptx/sec_alt_series.ptx b/ptx/sec_alt_series.ptx
index c4c648044..fa1fa2fcc 100644
--- a/ptx/sec_alt_series.ptx
+++ b/ptx/sec_alt_series.ptx
@@ -146,7 +146,7 @@
     the sum of the series.
   </p>
 
-  <figure xml:id="fig_alt_series_converge_a" vshift="0">
+  <figure xml:id="fig_alt_series_converge_a" vshift="-1">
     <caption>Illustrating convergence with the Alternating Series Test</caption>
   <!-- START figures/fig_alt_series_converge.tex -->
     <image width="47%">
diff --git a/ptx/sec_arc_length.ptx b/ptx/sec_arc_length.ptx
index 5abca48dd..893ec5552 100644
--- a/ptx/sec_arc_length.ptx
+++ b/ptx/sec_arc_length.ptx
@@ -331,7 +331,7 @@
           </md>.
         </p>
 
-        <figure xml:id="fig_arc1" vshift="-1">
+        <figure xml:id="fig_arc1" vshift="1">
           <caption>A graph of <m>f(x) = x^{3/2}</m> from <xref ref="ex_arc1"/></caption>
           <!-- START figures/fig_arc1.tex -->
           <image width="47%">
@@ -397,7 +397,7 @@
           </md>.
         </p>
 
-        <figure xml:id="fig_arc2" vshift="-1">
+        <figure xml:id="fig_arc2" vshift="2">
           <caption>A graph of <m>f(x) =\frac18x^2-\ln(x)</m> from <xref ref="ex_arc2"/></caption>
           <!-- START figures/fig_arc2.tex -->
           <image width="47%">
diff --git a/ptx/sec_center_of_mass.ptx b/ptx/sec_center_of_mass.ptx
index cf6c92ee7..c24eb117f 100644
--- a/ptx/sec_center_of_mass.ptx
+++ b/ptx/sec_center_of_mass.ptx
@@ -177,7 +177,7 @@
       That is, for a small enough subregion of <m>R</m>,
       the density across that region is almost constant.
     </p>
-    <aside vshift="0">
+    <aside vshift="2">
       <p>
         <em>Mass</em> and <em>weight</em> are different measures.
         Since they are scalar multiples of each other,
diff --git a/ptx/sec_conic_sections.ptx b/ptx/sec_conic_sections.ptx
index 996e8c474..c435910c6 100644
--- a/ptx/sec_conic_sections.ptx
+++ b/ptx/sec_conic_sections.ptx
@@ -1536,7 +1536,7 @@
             This is enough to make a good sketch.
           </p>
 
-          <figure xml:id="fig_conic5" vshift="-2.5">
+          <figure xml:id="fig_conic5" vshift="0">
             <caption>Graphing the hyperbola in <xref ref="ex_conic5"/></caption>
             <!-- START figures/fig_conic5.tex -->
             <image width="47%">
@@ -1623,7 +1623,7 @@
             </md>
           </p>
 
-          <figure xml:id="fig_conic6" vshift="-6">
+          <figure xml:id="fig_conic6" vshift="0">
             <caption>Graphing the hyperbola in <xref ref="ex_conic6"/></caption>
             <!-- START figures/fig_conic6.tex -->
             <image width="47%">
diff --git a/ptx/sec_def_int.ptx b/ptx/sec_def_int.ptx
index 07ac8efa0..5997a6508 100644
--- a/ptx/sec_def_int.ptx
+++ b/ptx/sec_def_int.ptx
@@ -667,7 +667,7 @@
   </p>
 
   <p>
-    <dl>
+    <dl width="narrow">
       <li>
         <title>1.</title>
         <p>
@@ -749,7 +749,7 @@
         <xref ref="fig_defint5"/>.
       </p>
 
-      <figure xml:id="fig_defint5" vshift="-2">
+      <figure xml:id="fig_defint5" vshift="1">
         <caption>A graph of a function in <xref ref="ex_defint5"/></caption>
         <image width="47%">
         <shortdescription>
diff --git a/ptx/sec_double_int_volume.ptx b/ptx/sec_double_int_volume.ptx
index a3c208bc6..fc9cfb30a 100644
--- a/ptx/sec_double_int_volume.ptx
+++ b/ptx/sec_double_int_volume.ptx
@@ -337,7 +337,7 @@
     This leads to a definition.
   </p>
 
-  <aside xml:id="note_doubleint" vshift="-1.5">
+  <aside xml:id="note_doubleint" vshift="-2.5">
     <title>Double integrals as limits of double sums</title>
 
     <p>
@@ -463,7 +463,7 @@
     the bounds depend on the value of <m>x</m>.
   </p>
 
-  <figure xml:id="fig_double_intro3" vshift="1.5">
+  <figure xml:id="fig_double_intro3" vshift="2">
     <caption>Finding volume under a surface by sweeping out a cross-sectional area</caption>
 
     <!-- START figures/figdouble_intro3_3D.asy -->
@@ -1027,7 +1027,7 @@
         Evaluate the double integral <m>\iint_Rf(x,y)\, dA</m>.
       </p>
 
-      <figure xml:id="fig_double3" vshift="1">
+      <figure xml:id="fig_double3" vshift="0">
         <caption>Finding the signed volume under a surface in <xref ref="ex_double3"/></caption>
 
         <!-- START figures/figdouble3_3D.asy -->
@@ -1439,7 +1439,7 @@
         shows the surface over <m>R</m>.
       </p>
 
-      <figure xml:id="fig_double6b" vshift="6">
+      <figure xml:id="fig_double6b" vshift="2">
         <caption>Showing the surface <m>z=f(x,y)</m> defined in <xref ref="ex_double6"/> over its region <m>R</m></caption>
 
         <!-- START figures/figdouble6b_3D.asy -->
diff --git a/ptx/sec_fluid_force.ptx b/ptx/sec_fluid_force.ptx
index 12050a097..f25fc9d98 100644
--- a/ptx/sec_fluid_force.ptx
+++ b/ptx/sec_fluid_force.ptx
@@ -552,7 +552,7 @@
               Thus the length function is <m>\ell(y) = 1/2y-(-1/2y) = y</m>.
             </p>
 
-            <figure xml:id="fig_fluid2c" vshift="0">
+            <figure xml:id="fig_fluid2c" vshift="-0.5">
               <caption>Sketching the triangular plate in <xref ref="ex_fluid2"/> with the convention that the base of the triangle is at <m>(0,0)</m></caption>
           <!-- START figures/fig_fluid2c.tex -->
               <image width="47%">
diff --git a/ptx/sec_graph_extreme_values.ptx b/ptx/sec_graph_extreme_values.ptx
index 927ca1d26..a51bb04a8 100644
--- a/ptx/sec_graph_extreme_values.ptx
+++ b/ptx/sec_graph_extreme_values.ptx
@@ -388,7 +388,7 @@
         At each of these points, evaluate <m>\fp</m>.
       </p>
 
-      <figure xml:id="fig_extval2" vshift="-0.5">
+      <figure xml:id="fig_extval2" vshift="0">
         <caption>A graph of <m>f(x) = (3x^4-4x^3-12x^2+5)/5</m> as in <xref ref="ex_extval2"/></caption>
           <!-- START figures/fig_extval2.tex -->
         <image width="47%">
@@ -445,7 +445,7 @@
         At each of these points, evaluate <m>\fp</m>.
       </p>
 
-      <figure xml:id="fig_extval3" vshift="-1.5">
+      <figure xml:id="fig_extval3" vshift="-0.5">
         <caption>A graph of <m>f(x) = (x-1)^{2/3}+2</m> as in <xref ref="ex_extval3"/></caption>
           <!-- START figures/fig_extval3.tex -->
         <image width="47%">
@@ -549,7 +549,7 @@
     </statement>
   </definition>
 
-  <aside xml:id="aside-graph-extreme-vocabulary3" vshift="1.25">
+  <aside xml:id="aside-graph-extreme-vocabulary3" vshift="2">
     <p>
       In this text we use <q>critical number</q> and <q>critical value</q>
       interchangeably. Other textbooks reserve the term <em>critical value</em>
@@ -628,8 +628,6 @@
     </matching>
   </exercise>
 
-
-
   <p>
     Be careful to understand that this theorem states
     <q>Relative extrema on open intervals occur at critical points.</q>
@@ -642,7 +640,7 @@
   </p>
 
   
-  <figure xml:id="fig_extreme4" vshift="-2">
+  <figure xml:id="fig_extreme4" vshift="1.5">
     <caption>A graph of <m>f(x)=x^3</m> which has a critical value of <m>x=0</m>, but no relative extrema</caption>
       <!-- START figures/fig_extreme4.tex -->
     <image width="47%">
@@ -1156,6 +1154,8 @@
     </p>
   </aside>
 
+  <enlarge-page skipsize="2"/>
+
   <p>
     We have seen that continuous functions on closed intervals always have a maximum and minimum value,
     and we have also developed a technique to find these values.
@@ -1888,6 +1888,8 @@
         </exercise>
       </exercisegroup>
 
+      <enlarge-page skipsize="2"/>
+
       <exercisegroup cols="2" xml:id="exset-graph-extreme-values-find">
         <introduction>
           <p>
diff --git a/ptx/sec_greensthm.ptx b/ptx/sec_greensthm.ptx
index 104242f2d..aedf38cfd 100644
--- a/ptx/sec_greensthm.ptx
+++ b/ptx/sec_greensthm.ptx
@@ -1178,7 +1178,7 @@
           that is, find the flux across <m>C</m> and show it is equal to the double integral of <m>\divv \vec F</m> over <m>R</m>.
         </p>
 
-        <figure xml:id="fig_div1" vshift="-4">
+        <figure xml:id="fig_div1" vshift="-5">
           <caption>The region <m>R</m> used in <xref ref="ex_div1"/></caption>
           <image width="47%">
             <shortdescription>A circle in the plane, plotted against a spiral vector field.</shortdescription>
@@ -1300,7 +1300,7 @@
           consider:
         </p>
 
-        <figure xml:id="fig_div2" vshift="0">
+        <figure xml:id="fig_div2" vshift="-1">
           <caption>As used in <xref ref="ex_div2"/>, the vector field has a divergence of 0 and the two paths only intersect at their initial and terminal points.</caption>
           <image width="47%">
             <shortdescription>Two curves in the plane between points A and B, and a vector field with many vortices.</shortdescription>
diff --git a/ptx/sec_int_comp_tests.ptx b/ptx/sec_int_comp_tests.ptx
index 19f58834d..b99d22357 100644
--- a/ptx/sec_int_comp_tests.ptx
+++ b/ptx/sec_int_comp_tests.ptx
@@ -275,7 +275,7 @@
           We can still use the integral test since a finite number of terms will not affect convergence of the series.
         </p>
 
-        <figure xml:id="fig_itest1" vshift="-1">
+        <figure xml:id="fig_itest1" vshift="-2">
           <caption>Plotting the sequence and series in <xref ref="ex_itest1"/></caption>
           <!-- START figures/fig_itest1.tex -->
           <image width="47%">
@@ -1675,88 +1675,83 @@
         </exercise>
       </exercisegroup>
 
-      <exercise label="ex-int-comp-test-multi1">
-        <!--<webwork xml:id="webwork-ex-int-comp-test-multi1">
-            <pg-code>
-            </pg-code>-->
-            <introduction>
-              <p>
-                Given that <m>\ds \infser a_n</m> converges,
-                state which of the following series converges,
-                may converge, or does not converge.
-              </p>
-            </introduction>
-
-            <task label="ex-int-comp-test-multi1a">
-              <statement>
-                <p>
-                  <m>\ds \infser \frac{a_n}n</m>
-                </p>
-              </statement>
-              <solution>
-                <p>
-                  Converges; use Direct Comparison Test as <m>\frac{a_n}{n}\lt n</m>.
-                </p>
-              </solution>
-            </task>
+      <exercisegroup cols="2" xml:id="ex-int-comp-test-multi1">
+        <introduction>
+          <p>
+            Given that <m>\ds \infser a_n</m> converges,
+            state which of the following series converges,
+            may converge, or does not converge.
+          </p>
+        </introduction>
 
-            <task xml:id="task-series-intcomp1" label="ex-int-comp-test-multi1b">
-              <statement>
-                <p>
-                  <m>\ds \infser a_n a_{n+1}</m>
-                </p>
-              </statement>
-              <solution>
-                <p>
-                  Converges; since original series converges,
-                  we know <m>\lim_{n\to\infty}a_n = 0</m>.
-                  Thus for large <m>n</m>, <m>a_na_{n+1} \lt a_n</m>.
-                </p>
-              </solution>
-            </task>
+        <exercise label="ex-int-comp-test-multi1a">
+          <statement>
+            <p>
+              <m>\ds \infser \frac{a_n}n</m>
+            </p>
+          </statement>
+          <solution>
+            <p>
+              Converges; use Direct Comparison Test as <m>\frac{a_n}{n}\lt n</m>.
+            </p>
+          </solution>
+        </exercise>
 
-            <task label="ex-int-comp-test-multi1c">
-              <statement>
-                <p>
-                  <m>\ds \infser (a_n)^2</m>
-                </p>
-              </statement>
-              <solution>
-                <p>
-                  Converges; similar logic to  so <m>(a_n)^2\lt a_n</m>.
-                </p>
-              </solution>
-            </task>
+        <exercise xml:id="task-series-intcomp1" label="ex-int-comp-test-multi1b">
+          <statement>
+            <p>
+              <m>\ds \infser a_n a_{n+1}</m>
+            </p>
+          </statement>
+          <solution>
+            <p>
+              Converges; since original series converges,
+              we know <m>\lim_{n\to\infty}a_n = 0</m>.
+              Thus for large <m>n</m>, <m>a_na_{n+1} \lt a_n</m>.
+            </p>
+          </solution>
+        </exercise>
 
-            <task label="ex-int-comp-test-multi1d">
-              <statement>
-                <p>
-                  <m>\ds \infser na_n</m>
-                </p>
-              </statement>
-              <solution>
-                <p>
-                  May converge;
-                  certainly <m>na_n  \gt  a_n</m> but that does not mean it does not converge.
-                </p>
-              </solution>
-            </task>
+        <exercise label="ex-int-comp-test-multi1c">
+          <statement>
+            <p>
+              <m>\ds \infser (a_n)^2</m>
+            </p>
+          </statement>
+          <solution>
+            <p>
+              Converges; similar logic to  so <m>(a_n)^2\lt a_n</m>.
+            </p>
+          </solution>
+        </exercise>
 
-            <task label="ex-int-comp-test-multi1e">
-              <statement>
-                <p>
-                  <m>\ds \infser \frac{1}{a_n}</m>
-                </p>
-              </statement>
-              <solution>
-                <p>
-                  Does not converge, using logic from <xref ref="task-series-intcomp1" text="custom">part</xref> and <m>n^{th}</m> Term Test.
-                </p>
-              </solution>
-            </task>
+        <exercise label="ex-int-comp-test-multi1d">
+          <statement>
+            <p>
+              <m>\ds \infser na_n</m>
+            </p>
+          </statement>
+          <solution>
+            <p>
+              May converge;
+              certainly <m>na_n  \gt  a_n</m> but that does not mean it does not converge.
+            </p>
+          </solution>
+        </exercise>
 
-        <!--</webwork>-->
-      </exercise>
+        <exercise label="ex-int-comp-test-multi1e">
+          <statement>
+            <p>
+              <m>\ds \infser \frac{1}{a_n}</m>
+            </p>
+          </statement>
+          <solution>
+            <p>
+              Does not converge, using logic from <xref ref="task-series-intcomp1" text="custom">part</xref> and <m>n^{th}</m> Term Test.
+            </p>
+          </solution>
+        </exercise>
+      </exercisegroup>
 
       <exercise label="ex-int-comp-test-multi2">
         <introduction>
diff --git a/ptx/sec_lhopitals_rule.ptx b/ptx/sec_lhopitals_rule.ptx
index 2d0dbb7cb..0120f06cc 100644
--- a/ptx/sec_lhopitals_rule.ptx
+++ b/ptx/sec_lhopitals_rule.ptx
@@ -511,7 +511,7 @@
                 This result is supported by the graph of
                 <m>f(x)=x^x</m> given in <xref ref="fig_LHR4"/>.
               </p>
-                <figure xml:id="fig_LHR4" vshift="2">
+                <figure xml:id="fig_LHR4" vshift="2.5">
                   <caption>A graph of <m>f(x)=x^x</m> supporting the fact that as <m>x\to 0^+</m>, <m>f(x)\to 1</m></caption>
                   <!-- START figures/fig_LHR4.tex -->
                   <image width="47%">
diff --git a/ptx/sec_limit_analytically.ptx b/ptx/sec_limit_analytically.ptx
index d62392149..c15f59659 100644
--- a/ptx/sec_limit_analytically.ptx
+++ b/ptx/sec_limit_analytically.ptx
@@ -667,7 +667,7 @@
         Later we will show that we can also consider <m>\theta \leq 0</m>.)
       </p>
 
-      <figure xml:id="fig_squeeze_sinx" vshift="-5.5">
+      <figure xml:id="fig_squeeze_sinx" vshift="-5.75">
         <caption>The unit circle and related triangles</caption>
         <!-- START figures/fig_squeeze1.tex -->
         <image width="47%">
diff --git a/ptx/sec_limit_continuity.ptx b/ptx/sec_limit_continuity.ptx
index b8f7cd198..d0bcf4eee 100644
--- a/ptx/sec_limit_continuity.ptx
+++ b/ptx/sec_limit_continuity.ptx
@@ -111,7 +111,7 @@
         Give the interval(s) on which <m>f</m> is continuous.
       </p>
 
-      <figure xml:id="fig_continuous1" vshift="3">
+      <figure xml:id="fig_continuous1" vshift="2.5">
         <caption>A graph of <m>f</m> in <xref ref="ex_contint1"/></caption>
         <!-- START figures/fig_continuous1.tex -->
         <image width="47%">
@@ -181,7 +181,7 @@
         <m>(0,3)</m> except at <m>x=1</m>.
         Therefore <m>f</m> is continuous on <m>(0,1)</m> and <m>(1,3)</m>.
       </p>
-      <aside xml:id="aside-limit-continuous-intervals" vshift="3.5">
+      <aside xml:id="aside-limit-continuous-intervals" vshift="3">
         <p>
           Our definition of continuity (currently) only applies to open intervals.
           After <xref ref="def_closed_continuity"/>,
@@ -213,7 +213,7 @@
         Give the intervals on which <m>f</m> is continuous.
       </p>
 
-      <figure xml:id="fig_continuous2" vshift="2">
+      <figure xml:id="fig_continuous2" vshift="1.5">
         <caption>A graph of the step function in <xref ref="ex_contint2"/></caption>
         <!-- START figures/fig_continuous2.tex -->
         <image width="47%">
@@ -359,7 +359,7 @@
     by considering the appropriate one-sided limits at the endpoints.
   </p>
 
-  <aside vshift="0">
+  <aside vshift="-2">
     <p>
       In this text, when we use the term <q>closed interval</q>,
       we mean an interval of the form <m>[a,b]</m>,
@@ -656,7 +656,7 @@
     <video youtube="GTiNiZT5ukg" label="vid_limit_con_prop"/>
   </figure>
 
-  <aside xml:id="aside-limit-continuity-collection-intervals" vshift="4.5">
+  <aside xml:id="aside-limit-continuity-collection-intervals" vshift="4">
     <p>
       We have defined what it means for a function to be continuous on an interval,
       but many functions, such as <m>f(x)=\tan(x)</m>,
@@ -805,7 +805,7 @@
         and <xref ref="thm_continuous_functions" text="global"/> as appropriate.
       </p>
 
-      <figure xml:id="fig_continuous3" vshift="1">
+      <figure xml:id="fig_continuous3" vshift="0">
         <caption>A graph of <m>f(x)=\sqrt{x-1}+\sqrt{5-x}</m></caption>
         <!-- START figures/fig_continuous3.tex -->
         <image width="47%">
@@ -1146,7 +1146,7 @@
       but we are guaranteed all values between <m>-10</m> and <m>5</m>. This concept is illustrated in <xref ref="fig_intermediate_value"/>.
     </p>
 
-    <figure xml:id="fig_intermediate_value" vshift="2">
+    <figure xml:id="fig_intermediate_value" vshift="0">
       <caption>Illustration of the Intermediate Value Theorem: the output <m>3</m> is in between <m>-10</m> and <m>5</m>,
       and therefore any continuous function on <m>[1,2]</m> with <m>f(1) = -10</m> and <m>f(2) = 5</m>
       will achieve the output <m>3</m> somewhere in <m>[1,2]</m></caption>
@@ -3207,7 +3207,7 @@
 
               <instruction>If <m>f(m)\gt 0</m> at the midpoint <m>m</m>, put <m>+</m> for the midpoint sign. If <m>f(m)\lt 0</m>, put <m>-</m> for the midpoint sign.</instruction>
               
-              <tabular>
+              <tabular component="web">
                 <row bottom="medium">
                   <cell>Iteration</cell>
                   <cell>Interval</cell>
@@ -3297,7 +3297,7 @@
 
               <instruction>If <m>f(m)\gt 0</m> at the midpoint <m>m</m>, put <m>+</m> for the midpoint sign. If <m>f(m)\lt 0</m>, put <m>-</m> for the midpoint sign.</instruction>
               
-              <tabular>
+              <tabular component="web">
                 <row bottom="medium">
                   <cell>Iteration</cell>
                   <cell>Interval</cell>
@@ -3387,7 +3387,7 @@
 
               <instruction>If <m>f(m)\gt 0</m> at the midpoint <m>m</m>, put <m>+</m> for the midpoint sign. If <m>f(m)\lt 0</m>, put <m>-</m> for the midpoint sign.</instruction>
               
-              <tabular>
+              <tabular component="web">
                 <row bottom="medium">
                   <cell>Iteration</cell>
                   <cell>Interval</cell>
@@ -3477,7 +3477,7 @@
 
               <instruction>If <m>f(m)\gt 0</m> at the midpoint <m>m</m>, put <m>+</m> for the midpoint sign. If <m>f(m)\lt 0</m>, put <m>-</m> for the midpoint sign.</instruction>
               
-              <tabular>
+              <tabular component="web">
                 <row bottom="medium">
                   <cell>Iteration</cell>
                   <cell>Interval</cell>
diff --git a/ptx/sec_limit_def.ptx b/ptx/sec_limit_def.ptx
index f72e247d4..faafa93ae 100644
--- a/ptx/sec_limit_def.ptx
+++ b/ptx/sec_limit_def.ptx
@@ -485,7 +485,7 @@
     without using the <m>\varepsilon</m>-<m>\delta</m> definition.
   </p>
 
-  <aside vshift="2.5">
+  <aside vshift="2.75">
     <p>
       At this point, you may well be wondering:
       if using the <m>\varepsilon</m>-<m>\delta</m> definition is so hard,
@@ -594,7 +594,7 @@
         <m>f(x)</m> will be within <m>\varepsilon</m> of <m>4</m>.
       </p>
 
-      <figure xml:id="fig_limit_eover5" vshift="3">
+      <figure xml:id="fig_limit_eover5" vshift="2.75">
         <caption>Choosing <m>\delta = \varepsilon/5</m> in <xref ref="ex_compute_lim2"/></caption>
         <!-- START figures/fig_limit_proof2a.tex -->
         <image width="47%">
@@ -949,7 +949,7 @@
           \delta = \min\{\abs{\ln(1-\varepsilon)}, \ln(1+\varepsilon)\} = \ln(1+\varepsilon)\text{.} \quad \text{(See marginal note.)}
         </md>
       </p>
-      <aside xml:id="aside-limit-def-min-explain" vshift="2">
+      <aside xml:id="aside-limit-def-min-explain" vshift="1">
         <p>
         Recall <m>\ln 1= 0</m> and
         <m>\ln x\lt 0</m> when <m>0\lt x\lt 1</m>.
diff --git a/ptx/sec_limit_onesided.ptx b/ptx/sec_limit_onesided.ptx
index 725eaa460..2f794a779 100644
--- a/ptx/sec_limit_onesided.ptx
+++ b/ptx/sec_limit_onesided.ptx
@@ -694,7 +694,7 @@
         </ol>
       </p>
 
-      <figure xml:id="fig_onesidedc" vshift="1">
+      <figure xml:id="fig_onesidedc" vshift="1.1">
         <caption>Graphing <m>f</m> in <xref ref="ex_onesidec"/></caption>
         <!-- START figures/fig_one_sidedlimit3.tex -->
         <image width="47%">
@@ -770,7 +770,7 @@
         </ol>
       </p>
 
-      <figure xml:id="fig_onesidedd" vshift="2">
+      <figure xml:id="fig_onesidedd" vshift="1.5">
         <caption>Graphing <m>f</m> in <xref ref="ex_onesided"/></caption>
         <!-- START figures/fig_one_sidedlimit4.tex -->
         <image width="47%">
diff --git a/ptx/sec_lines.ptx b/ptx/sec_lines.ptx
index 366702b34..85a79a0e3 100644
--- a/ptx/sec_lines.ptx
+++ b/ptx/sec_lines.ptx
@@ -596,7 +596,7 @@
 
         <pagebreak-latex component="novideo"/>
         
-        <figure xml:id="fig_lines2" vshift="-1">
+        <figure xml:id="fig_lines2" vshift="-3">
           <caption>Sketching the lines from <xref ref="ex_lines2"/></caption>
 
           <!-- START figures/figlines2_3D.asy -->
diff --git a/ptx/sec_multi_extreme_values.ptx b/ptx/sec_multi_extreme_values.ptx
index 6b4f55efe..31ca2db3c 100644
--- a/ptx/sec_multi_extreme_values.ptx
+++ b/ptx/sec_multi_extreme_values.ptx
@@ -357,7 +357,7 @@
           we consider the graph of <m>f</m> in <xref ref="fig_multi_extreme3"/>.
         </p>
 
-        <figure xml:id="fig_multi_extreme3" vshift="-2">
+        <figure xml:id="fig_multi_extreme3" vshift="1">
           <caption>The surface in <xref ref="ex_multi_extreme3"/> with both critical points marked</caption>
 
           <!-- START figures/figmulti_extreme3_3D.asy -->
diff --git a/ptx/sec_multi_tangent.ptx b/ptx/sec_multi_tangent.ptx
index b3dbcb290..8e1f912e6 100644
--- a/ptx/sec_multi_tangent.ptx
+++ b/ptx/sec_multi_tangent.ptx
@@ -827,7 +827,7 @@
           </md>
         </p>
 
-        <figure xml:id="fig_tpl5" vshift="2">
+        <figure xml:id="fig_tpl5" vshift="-1">
           <caption>Graphing the surface in <xref ref="ex_tpl5"/> along with points 4 units from the surface</caption>
 
           <!-- START figures/figtpl5_3D.asy -->
@@ -919,7 +919,7 @@
       <em>tangent</em> to <m>f</m> at <m>P</m>.
     </p>
 
-    <aside vshift="-1.5">
+    <aside vshift="-3">
       <p>
         When we introduced the tangent plane in <xref ref="sec_partial_derivatives"/>,
         we computed the normal vector to be <m>\vec{n}=\la -f_x(x_0,y_0),-f_y(x_0,y_0),1\ra</m>.
@@ -971,7 +971,7 @@
           The surface <m>z=-x^2-y^2+2</m> and tangent plane are graphed in <xref ref="fig_tpl6"/>.
         </p>
 
-        <figure xml:id="fig_tpl6" vshift="0">
+        <figure xml:id="fig_tpl6" vshift="-1">
           <caption>Graphing a surface with tangent plane from <xref ref="ex_tpl6"/></caption>
 
           <!-- START figures/figtpl6_3D.asy -->
diff --git a/ptx/sec_par_calc.ptx b/ptx/sec_par_calc.ptx
index 63db3a8df..295d16c6e 100644
--- a/ptx/sec_par_calc.ptx
+++ b/ptx/sec_par_calc.ptx
@@ -370,7 +370,7 @@
                 any line that passes through the center of a circle intersects the circle at right angles.
               </p>
 
-              <figure xml:id="fig_parcalc2" vshift="-1">
+              <figure xml:id="fig_parcalc2" vshift="1">
                 <caption>Illustrating how a circle's normal lines pass through its center</caption>
             <!-- START figures/fig_parcalc2.tex -->
                 <image width="47%">
@@ -428,7 +428,7 @@
           <m>y=\sin^3(t)</m> at <m>t=0</m>,
           shown in <xref ref="fig_parcalc3"/>.
         </p>
-        <figure xml:id="fig_parcalc3" vshift="-10">
+        <figure xml:id="fig_parcalc3" vshift="-5">
           <caption>A graph of an astroid</caption>
           <!-- START figures/fig_planecurve1.tex -->
           <image width="47%">
diff --git a/ptx/sec_polar.ptx b/ptx/sec_polar.ptx
index 8bc98c21a..3106688ac 100644
--- a/ptx/sec_polar.ptx
+++ b/ptx/sec_polar.ptx
@@ -814,7 +814,7 @@
       in <xref ref="fig_polar4c"/>.
     </p>
 
-    <figure xml:id="fig_polar4c" vshift="4">
+    <figure xml:id="fig_polar4c" vshift="5">
       <caption>Using  technology to graph a polar function</caption>
       <!-- START figures/fig_polar4c.tex -->
       <image width="47%">
@@ -874,7 +874,7 @@
           we numbered each point in the table and on the graph.
         </p>
 
-        <figure xml:id="fig_polar5table" vshift="-1">
+        <figure xml:id="fig_polar5table" vshift="0">
           <caption>Table of points for plotting a polar curve in <xref ref="ex_polar5"/></caption>
           <tabular halign="center">
             <row bottom="minor"><cell>Pt.</cell><cell><m>\theta</m></cell><cell><m>\cos(2\theta)</m></cell></row>
@@ -1213,682 +1213,684 @@
       and is left as a problem in the Exercise section.
     </p>
 
-    <p>
-      <em> Gallery of Polar Curves</em>
-    </p>
-
-    <p>
-      There are a number of basic and
-      <q>classic</q> polar curves,
-      famous for their beauty and/or applicability to the sciences.
-          <idx><h>polar</h><h>function!gallery of graphs</h></idx>
-      This section ends with a small gallery of some of these graphs.
-      We encourage the reader to understand how these graphs are formed,
-      and to investigate with technology other types of polar functions.
-    </p>
-
-    <figure xml:id="fig_polar_lines" hstretch="450" hskip="120">
-      <caption>Lines in polar coordinates</caption>
-      <sidebyside valign="bottom" widths="23% 23% 23% 23%">
-        <figure xml:id="fig_polar_lines1">
-          <caption>Through the origin: <m>\theta = \alpha</m></caption>
-          <!-- START figures/fig_polarline1.tex -->
-          <image>
-            <shortdescription>A line through the origin with positive slope.</shortdescription>
-            <description>
-              <p>
-                A line through the origin is shown on a set of rectangular axes.
-                Also shown is an angle <m>\alpha</m>, measured from the positive <m>x</m> axis to the line.
-              </p>
-            </description>
-            <latex-image label="img_polar_lines1">
+    <enlarge-page skipsize="2"/>
 
-            \begin{tikzpicture}
+    <paragraphs>
+      <title>Gallery of Polar Curves</title>
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+      <p>
+        There are a number of basic and
+        <q>classic</q> polar curves,
+        famous for their beauty and/or applicability to the sciences.
+            <idx><h>polar</h><h>function!gallery of graphs</h></idx>
+        This section ends with a small gallery of some of these graphs.
+        We encourage the reader to understand how these graphs are formed,
+        and to investigate with technology other types of polar functions.
+      </p>
 
-            \draw [thick,firstcolor,rotate=50] (-2.1,0) -- (2.1,0);
+      <figure xml:id="fig_polar_lines" hstretch="450" hskip="120">
+        <caption>Lines in polar coordinates</caption>
+        <sidebyside valign="bottom" widths="23% 23% 23% 23%">
+          <figure xml:id="fig_polar_lines1">
+            <caption>Through the origin: <m>\theta = \alpha</m></caption>
+            <!-- START figures/fig_polarline1.tex -->
+            <image>
+              <shortdescription>A line through the origin with positive slope.</shortdescription>
+              <description>
+                <p>
+                  A line through the origin is shown on a set of rectangular axes.
+                  Also shown is an angle <m>\alpha</m>, measured from the positive <m>x</m> axis to the line.
+                </p>
+              </description>
+              <latex-image label="img_polar_lines1">
 
-            \draw [-&gt;] (.5,0) arc (0:50:.5);
-            \draw [rotate=25] (.7,0) node { $\alpha$};
+              \begin{tikzpicture}
 
-            \end{tikzpicture}
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarline1.tex END -->
-        </figure>
-        <figure xml:id="fig_polar_lines2">
-          <caption>Horizontal line: <m>r=a\csc(\theta)</m></caption>
-          <!-- START figures/fig_polarline2.tex -->
-          <image>
-            <shortdescription>A horizontal line.</shortdescription>
-            <description>
-              <p>
-                The graph is that of a horizontal line, plotted on a set of rectangular axes.
-                The graph is labeled with the value <m>a</m>, which is the distance from the <m>x</m> axis to the line.
-              </p>
-            </description>
-            <latex-image label="img_polar_lines2">
+              \draw [thick,firstcolor,rotate=50] (-2.1,0) -- (2.1,0);
 
-            \begin{tikzpicture}
+              \draw [-&gt;] (.5,0) arc (0:50:.5);
+              \draw [rotate=25] (.7,0) node { $\alpha$};
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \end{tikzpicture}
 
-            \draw [thick,firstcolor] (-2,.6) -- (2,.6);
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarline1.tex END -->
+          </figure>
+          <figure xml:id="fig_polar_lines2">
+            <caption>Horizontal line: <m>r=a\csc(\theta)</m></caption>
+            <!-- START figures/fig_polarline2.tex -->
+            <image>
+              <shortdescription>A horizontal line.</shortdescription>
+              <description>
+                <p>
+                  The graph is that of a horizontal line, plotted on a set of rectangular axes.
+                  The graph is labeled with the value <m>a</m>, which is the distance from the <m>x</m> axis to the line.
+                </p>
+              </description>
+              <latex-image label="img_polar_lines2">
 
-            \draw (-.2,.3) node { $a\left\{\rule[-.23cm]{0pt}{.23cm}\right.$};
+              \begin{tikzpicture}
 
-            \end{tikzpicture}
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarline2.tex END -->
-        </figure>
+              \draw [thick,firstcolor] (-2,.6) -- (2,.6);
 
-        <figure xml:id="fig_polar_lines3">
-          <caption>Vertical line: <m>r=a\sec(\theta)</m></caption>
-          <!-- START figures/fig_polarline4.tex -->
-          <image>
-            <shortdescription>A vertical line.</shortdescription>
-            <description>
-              <p>
-                A vertical line is plotted against a set of rectangular axes.
-                The distance from the line to the <m>y</m> axis is labeled <m>a</m>.
-              </p>
-            </description>
-            <latex-image label="img_polar_lines3">
+              \draw (-.2,.3) node { $a\left\{\rule[-.23cm]{0pt}{.23cm}\right.$};
 
-            \begin{tikzpicture}
+              \end{tikzpicture}
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarline2.tex END -->
+          </figure>
+
+          <figure xml:id="fig_polar_lines3">
+            <caption>Vertical line: <m>r=a\sec(\theta)</m></caption>
+            <!-- START figures/fig_polarline4.tex -->
+            <image>
+              <shortdescription>A vertical line.</shortdescription>
+              <description>
+                <p>
+                  A vertical line is plotted against a set of rectangular axes.
+                  The distance from the line to the <m>y</m> axis is labeled <m>a</m>.
+                </p>
+              </description>
+              <latex-image label="img_polar_lines3">
 
-            \draw [thick,firstcolor] (.6,-2) -- (.6,2);
+              \begin{tikzpicture}
 
-            \draw (.3,.2) node { $\overbrace{\rule{.55cm}{0pt}}$};
-            \draw (.3,.4) node { $a$};
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \end{tikzpicture}
+              \draw [thick,firstcolor] (.6,-2) -- (.6,2);
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarline4.tex END -->
-        </figure>
-        <figure xml:id="fig_polar_lines4">
-          <caption>Not through origin: <m>\ds r=\frac{b}{\sin(\theta) -m\cos(\theta)}</m></caption>
-          <!-- START figures/fig_polarline3.tex -->
-          <image>
-            <shortdescription>A line with positive slope m, and y intercept b.</shortdescription>
-            <description>
-              <p>
-                A line is plotted against a set of rectangular axes.
-                The line has a positive slope <m>m</m>, which is indicated next to the line.
-                Also shown is a distance <m>b</m> from the origin to the <m>y</m> intercept of the line,
-                indicating that this particular line does not pass through the origin.
-              </p>
-            </description>
-            <latex-image label="img_polar_lines4">
+              \draw (.3,.2) node { $\overbrace{\rule{.55cm}{0pt}}$};
+              \draw (.3,.4) node { $a$};
 
-            \begin{tikzpicture}
+              \end{tikzpicture}
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarline4.tex END -->
+          </figure>
+          <figure xml:id="fig_polar_lines4">
+            <caption>Not through origin: <m>\ds r=\frac{b}{\sin(\theta) -m\cos(\theta)}</m></caption>
+            <!-- START figures/fig_polarline3.tex -->
+            <image>
+              <shortdescription>A line with positive slope m, and y intercept b.</shortdescription>
+              <description>
+                <p>
+                  A line is plotted against a set of rectangular axes.
+                  The line has a positive slope <m>m</m>, which is indicated next to the line.
+                  Also shown is a distance <m>b</m> from the origin to the <m>y</m> intercept of the line,
+                  indicating that this particular line does not pass through the origin.
+                </p>
+              </description>
+              <latex-image label="img_polar_lines4">
 
-            \draw [thick,firstcolor,shift={(0,.6)},rotate=50] (-2.1,0) -- (1.7,0) node [pos=.82,rotate=50,black,shift={(0,-5pt)}] { slope $=m$};
+              \begin{tikzpicture}
 
-            \draw (.2,.3) node { $\left.\rule[-.23cm]{0pt}{.23cm}\right\}b$};
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \end{tikzpicture}
+              \draw [thick,firstcolor,shift={(0,.6)},rotate=50] (-2.1,0) -- (1.7,0) node [pos=.82,rotate=50,black,shift={(0,-5pt)}] { slope $=m$};
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarline3.tex END -->
-        </figure>
-      </sidebyside>
-    </figure>
+              \draw (.2,.3) node { $\left.\rule[-.23cm]{0pt}{.23cm}\right\}b$};
 
-    <figure xml:id="fig_polar_circle_spiral" hstretch="450" hskip="120">
-      <caption>Circles and Spirals</caption>
-      <sidebyside valign="bottom" widths="23% 23% 23% 23%">
-        <figure xml:id="fig_polar_circle1">
-          <caption>Centered on <m>x</m>-axis: <m>r=a\cos(\theta)</m></caption>
-          <!-- START figures/fig_polarcircle1.tex -->
-          <image>
-            <shortdescription>A circle centered on the positive x axis and passing through the origin.</shortdescription>
-            <description>
-              <p>
-                A circle is shown, with its center on the positive <m>x</m> axis.
-                The circle passes through the origin, and the diameter of the circle is labeled as <m>a</m>.
-                This suggests that the circle has center <m>(a/2,0)</m> and radius <m>a/2</m>.
-              </p>
-            </description>
-            <latex-image label="img_polar_circle1">
+              \end{tikzpicture}
 
-            \begin{tikzpicture}
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarline3.tex END -->
+          </figure>
+        </sidebyside>
+      </figure>
+
+      <figure xml:id="fig_polar_circle_spiral" hstretch="450" hskip="120">
+        <caption>Circles and Spirals</caption>
+        <sidebyside valign="bottom" widths="23% 23% 23% 23%">
+          <figure xml:id="fig_polar_circle1">
+            <caption>Centered on <m>x</m>-axis: <m>r=a\cos(\theta)</m></caption>
+            <!-- START figures/fig_polarcircle1.tex -->
+            <image>
+              <shortdescription>A circle centered on the positive x axis and passing through the origin.</shortdescription>
+              <description>
+                <p>
+                  A circle is shown, with its center on the positive <m>x</m> axis.
+                  The circle passes through the origin, and the diameter of the circle is labeled as <m>a</m>.
+                  This suggests that the circle has center <m>(a/2,0)</m> and radius <m>a/2</m>.
+                </p>
+              </description>
+              <latex-image label="img_polar_circle1">
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \begin{tikzpicture}
 
-            \draw [thick,firstcolor] (.9,0) circle (.9);
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \draw (.9,.1) node { $\overbrace{\rule{1.7cm}{0cm}}$};
-            \draw (.9,.3) node { $a$};
+              \draw [thick,firstcolor] (.9,0) circle (.9);
 
-            \end{tikzpicture}
+              \draw (.9,.1) node { $\overbrace{\rule{1.7cm}{0cm}}$};
+              \draw (.9,.3) node { $a$};
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarcircle1.tex END -->
-        </figure>
-        <figure xml:id="fig_polar_circle2">
-          <caption>Centered on <m>y</m>-axis: <m>r=a\sin(\theta)</m></caption>
-          <!-- START figures/fig_polarcircle2.tex -->
-          <image>
-            <shortdescription>A circle centered on the positive y axis and passing through the origin.</shortdescription>
-            <description>
-              <p>
-                A circle is shown, with its center on the positive <m>y</m> axis.
-                The circle passes through the origin, and the diameter of the circle is labeled as <m>a</m>.
-                This suggests that the circle has center <m>(0,a/2)</m> and radius <m>a/2</m>.
-              </p>
-            </description>
-            <latex-image label="img_polar_circle2">
+              \end{tikzpicture}
 
-            \begin{tikzpicture}
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarcircle1.tex END -->
+          </figure>
+          <figure xml:id="fig_polar_circle2">
+            <caption>Centered on <m>y</m>-axis: <m>r=a\sin(\theta)</m></caption>
+            <!-- START figures/fig_polarcircle2.tex -->
+            <image>
+              <shortdescription>A circle centered on the positive y axis and passing through the origin.</shortdescription>
+              <description>
+                <p>
+                  A circle is shown, with its center on the positive <m>y</m> axis.
+                  The circle passes through the origin, and the diameter of the circle is labeled as <m>a</m>.
+                  This suggests that the circle has center <m>(0,a/2)</m> and radius <m>a/2</m>.
+                </p>
+              </description>
+              <latex-image label="img_polar_circle2">
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \begin{tikzpicture}
 
-            \draw [thick,firstcolor] (0,.9) circle (.9);
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \draw (-.2,.9) node { $a\left\{\rule[-.8cm]{0cm}{0.8cm}\right.$};
+              \draw [thick,firstcolor] (0,.9) circle (.9);
 
-            \end{tikzpicture}
+              \draw (-.2,.9) node { $a\left\{\rule[-.8cm]{0cm}{0.8cm}\right.$};
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarcircle2.tex END -->
-        </figure>
-        <figure xml:id="fig_polar_circle3">
-          <caption>Centered on origin: <m>r=a</m></caption>
-          <!-- START figures/fig_polarcircle3.tex -->
-          <image>
-            <shortdescription>A circle centered at the origin.</shortdescription>
-            <description>
-              <p>
-                On a set of rectangular axes, a circle centered at the origin is plotted.
-                The radius <m>a</m> of the circle is labeled.
-              </p>
-            </description>
-            <latex-image label="img_polar_circle3">
+              \end{tikzpicture}
 
-            \begin{tikzpicture}
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarcircle2.tex END -->
+          </figure>
+          <figure xml:id="fig_polar_circle3">
+            <caption>Centered on origin: <m>r=a</m></caption>
+            <!-- START figures/fig_polarcircle3.tex -->
+            <image>
+              <shortdescription>A circle centered at the origin.</shortdescription>
+              <description>
+                <p>
+                  On a set of rectangular axes, a circle centered at the origin is plotted.
+                  The radius <m>a</m> of the circle is labeled.
+                </p>
+              </description>
+              <latex-image label="img_polar_circle3">
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \begin{tikzpicture}
 
-            \draw [thick,firstcolor] (0,0) circle (.9);
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \draw (.45,.1) node { $\overbrace{\rule{.8cm}{0cm}}$};
-            \draw (.45,.3) node { $a$};
+              \draw [thick,firstcolor] (0,0) circle (.9);
 
-            \end{tikzpicture}
+              \draw (.45,.1) node { $\overbrace{\rule{.8cm}{0cm}}$};
+              \draw (.45,.3) node { $a$};
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarcircle3.tex END -->
-        </figure>
-        <figure xml:id="fig_polar_spiral">
-          <caption>Archimedean spiral: <m>r=\theta</m></caption>
-          <!-- START figures/fig_polarspiral.tex -->
-          <image>
-            <shortdescription>A counter-clockwise spiral that begins at the origin.</shortdescription>
-            <description>
-              <p>
-                The curve begins at the origin and spirals outward, moving in a counter-clockwise direction.
-                The distance from the curve to the origin increases with the angle,
-                and three full revolutions of the spiral are shown.
-              </p>
+              \end{tikzpicture}
 
-              <p>
-                The appearance of the curve is not unlike that of a snail's shell.
-              </p>
-            </description>
-            <latex-image label="img_polar_spiral">
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarcircle3.tex END -->
+          </figure>
+          <figure xml:id="fig_polar_spiral">
+            <caption>Archimedean spiral: <m>r=\theta</m></caption>
+            <!-- START figures/fig_polarspiral.tex -->
+            <image>
+              <shortdescription>A counter-clockwise spiral that begins at the origin.</shortdescription>
+              <description>
+                <p>
+                  The curve begins at the origin and spirals outward, moving in a counter-clockwise direction.
+                  The distance from the curve to the origin increases with the angle,
+                  and three full revolutions of the spiral are shown.
+                </p>
 
-            \begin{tikzpicture}
+                <p>
+                  The appearance of the curve is not unlike that of a snail's shell.
+                </p>
+              </description>
+              <latex-image label="img_polar_spiral">
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \begin{tikzpicture}
 
-            \draw [thick,firstcolor,domain=0:18.85,samples=200] plot ({cos(deg(\x))*(\x/9.5)},{sin(deg(\x))*(\x/9.5)});
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \end{tikzpicture}
+              \draw [thick,firstcolor,domain=0:18.85,samples=200] plot ({cos(deg(\x))*(\x/9.5)},{sin(deg(\x))*(\x/9.5)});
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarspiral.tex END -->
-        </figure>
-      </sidebyside>
-    </figure>
+              \end{tikzpicture}
 
-    <figure xml:id="fig_polar_limacons" hstretch="450" hskip="120">
-      <caption>Limaçons</caption>
-      <sidebyside valign="bottom" widths="23% 23% 23% 23%">
-        <figure xml:id="fig_polar_limacon1">
-          <caption>With inner loop: <m>\ds \frac ab \lt  1</m></caption>
-          <!-- START figures/fig_polarlimacon1.tex -->
-          <image>
-            <shortdescription>A limaçon curve with a loop at the origin, and symmetric about the x axis.</shortdescription>
-            <description>
-              <p>
-                The first of several curves in the <q>limaçcon</q> family.
-                The curve intersects the <m>x</m> axis three times: at the origin, which it passes through twice,
-                and at two other points on the positive <m>x</m> axis.
-              </p>
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarspiral.tex END -->
+          </figure>
+        </sidebyside>
+      </figure>
+
+      <figure xml:id="fig_polar_limacons" hstretch="450" hskip="120">
+        <caption>Limaçons</caption>
+        <sidebyside valign="bottom" widths="23% 23% 23% 23%">
+          <figure xml:id="fig_polar_limacon1">
+            <caption>With inner loop: <m>\ds \frac ab \lt  1</m></caption>
+            <!-- START figures/fig_polarlimacon1.tex -->
+            <image>
+              <shortdescription>A limaçon curve with a loop at the origin, and symmetric about the x axis.</shortdescription>
+              <description>
+                <p>
+                  The first of several curves in the <q>limaçcon</q> family.
+                  The curve intersects the <m>x</m> axis three times: at the origin, which it passes through twice,
+                  and at two other points on the positive <m>x</m> axis.
+                </p>
 
-              <p>
-                The curve consists of two loops that are joined at the origin.
-                The larger, outer loop passes through the <m>x</m> intercept with the larger value of <m>x</m>.
-                It is somewhat heart-shaped, with a cusp at the origin.
-              </p>
+                <p>
+                  The curve consists of two loops that are joined at the origin.
+                  The larger, outer loop passes through the <m>x</m> intercept with the larger value of <m>x</m>.
+                  It is somewhat heart-shaped, with a cusp at the origin.
+                </p>
 
-              <p>
-                The smaller curve lies inside the larger curve, and is shaped like a teardrop.
-                The two curves join together in such a way that, although each individually has a cusp,
-                the curve as a whole is traced out smoothly, with the two cusps occurring at the origin,
-                where the curve intersects itself.
-              </p>
-            </description>
-            <latex-image label="img_polar_limacon1">
+                <p>
+                  The smaller curve lies inside the larger curve, and is shaped like a teardrop.
+                  The two curves join together in such a way that, although each individually has a cusp,
+                  the curve as a whole is traced out smoothly, with the two cusps occurring at the origin,
+                  where the curve intersects itself.
+                </p>
+              </description>
+              <latex-image label="img_polar_limacon1">
 
-            \begin{tikzpicture}
+              \begin{tikzpicture}
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \draw [thick,firstcolor,domain=0:360,samples=90] plot ({cos(\x)*(.6+1.2*cos(\x))},{sin(\x)*(.6+1.2*cos(\x))});
+              \draw [thick,firstcolor,domain=0:360,samples=90] plot ({cos(\x)*(.6+1.2*cos(\x))},{sin(\x)*(.6+1.2*cos(\x))});
 
-            \end{tikzpicture}
+              \end{tikzpicture}
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarlimacon1.tex END -->
-        </figure>
-        <figure xml:id="fig_polar_limacon2">
-          <caption>Cardioid: <m>\ds \frac ab=1</m></caption>
-          <!-- START figures/fig_polarlimacon2.tex -->
-          <image>
-            <shortdescription>A heart-shaped curve in the limaçon family, known as a cardioid.</shortdescription>
-            <description>
-              <p>
-                This is also a limaçon curve, and it is again symmetric about the <m>x</m> axis.
-                Its appearance is similar to the previous curve, but with the inner loop removed.
-              </p>
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarlimacon1.tex END -->
+          </figure>
+          <figure xml:id="fig_polar_limacon2">
+            <caption>Cardioid: <m>\ds \frac ab=1</m></caption>
+            <!-- START figures/fig_polarlimacon2.tex -->
+            <image>
+              <shortdescription>A heart-shaped curve in the limaçon family, known as a cardioid.</shortdescription>
+              <description>
+                <p>
+                  This is also a limaçon curve, and it is again symmetric about the <m>x</m> axis.
+                  Its appearance is similar to the previous curve, but with the inner loop removed.
+                </p>
 
-              <p>
-                The resulting cusp at the origin gives this curve a heart-like shape;
-                as a result, the curve is also known as a cardioid.
-              </p>
-            </description>
-            <latex-image label="img_polar_limacon2">
+                <p>
+                  The resulting cusp at the origin gives this curve a heart-like shape;
+                  as a result, the curve is also known as a cardioid.
+                </p>
+              </description>
+              <latex-image label="img_polar_limacon2">
 
-            \begin{tikzpicture}
+              \begin{tikzpicture}
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \draw [thick,firstcolor,domain=0:360,samples=90] plot ({cos(\x)*(.9+.9*cos(\x))},{sin(\x)*(.9+.9*cos(\x))});
+              \draw [thick,firstcolor,domain=0:360,samples=90] plot ({cos(\x)*(.9+.9*cos(\x))},{sin(\x)*(.9+.9*cos(\x))});
 
-            \end{tikzpicture}
+              \end{tikzpicture}
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarlimacon2.tex END -->
-        </figure>
-        <figure xml:id="fig_polar_limacon3">
-          <caption>Dimpled: <m>\ds 1\lt \frac ab \lt 2</m></caption>
-          <!-- START figures/fig_polarlimacon3.tex -->
-          <image>
-            <shortdescription>A dimpled limaçon curve.</shortdescription>
-            <description>
-              <p>
-                A third curve in the limaçon family, also symmetric about the <m>x</m> axis.
-                This curve does not pass through the origin.
-                It has two <m>x</m> intercepts, one positive, and one negative.
-                The positive <m>x</m> intercept has a larger absolute value (it is further from the origin).
-              </p>
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarlimacon2.tex END -->
+          </figure>
+          <figure xml:id="fig_polar_limacon3">
+            <caption>Dimpled: <m>\ds 1\lt \frac ab \lt 2</m></caption>
+            <!-- START figures/fig_polarlimacon3.tex -->
+            <image>
+              <shortdescription>A dimpled limaçon curve.</shortdescription>
+              <description>
+                <p>
+                  A third curve in the limaçon family, also symmetric about the <m>x</m> axis.
+                  This curve does not pass through the origin.
+                  It has two <m>x</m> intercepts, one positive, and one negative.
+                  The positive <m>x</m> intercept has a larger absolute value (it is further from the origin).
+                </p>
 
-              <p>
-                To the right of the <m>y</m> axis, the curve appears to be almost oval-like in shape.
-                But as it crosses to the left of the <m>y</m> axis, it begins to bend more sharply toward the second <m>x</m> intercept.
-                On this side, the curve bends inward, forming a <q>dimple</q>, or dent.
-                The dent is smooth, however, and is not a cusp.
-              </p>
-            </description>
-            <latex-image label="img_polar_limacon3">
+                <p>
+                  To the right of the <m>y</m> axis, the curve appears to be almost oval-like in shape.
+                  But as it crosses to the left of the <m>y</m> axis, it begins to bend more sharply toward the second <m>x</m> intercept.
+                  On this side, the curve bends inward, forming a <q>dimple</q>, or dent.
+                  The dent is smooth, however, and is not a cusp.
+                </p>
+              </description>
+              <latex-image label="img_polar_limacon3">
 
-            \begin{tikzpicture}
+              \begin{tikzpicture}
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \draw [thick,firstcolor,domain=0:360,samples=90] plot ({cos(\x)*(1+.8*cos(\x))},{sin(\x)*(1+.8*cos(\x))});
+              \draw [thick,firstcolor,domain=0:360,samples=90] plot ({cos(\x)*(1+.8*cos(\x))},{sin(\x)*(1+.8*cos(\x))});
 
-            \end{tikzpicture}
+              \end{tikzpicture}
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarlimacon3.tex END -->
-        </figure>
-        <figure xml:id="fig_polar_limacon4">
-          <caption>Convex: <m>\ds \frac ab \gt 2</m></caption>
-          <!-- START figures/fig_polarlimacon4.tex -->
-          <image>
-            <shortdescription>A convex limaçon curve.</shortdescription>
-            <description>
-              <p>
-                A fourth limaçon curve. It is also symmetric about the <m>x</m> axis.
-                Like the dimpled limaçon, it has two <m>x</m> intercepts and does not pass through the origin.
-              </p>
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarlimacon3.tex END -->
+          </figure>
+          <figure xml:id="fig_polar_limacon4">
+            <caption>Convex: <m>\ds \frac ab \gt 2</m></caption>
+            <!-- START figures/fig_polarlimacon4.tex -->
+            <image>
+              <shortdescription>A convex limaçon curve.</shortdescription>
+              <description>
+                <p>
+                  A fourth limaçon curve. It is also symmetric about the <m>x</m> axis.
+                  Like the dimpled limaçon, it has two <m>x</m> intercepts and does not pass through the origin.
+                </p>
 
-              <p>
-                Unlike the dimpled limaçon, to the left of the <m>y</m> axis, the curve flattens out,
-                but does not bend inward.
-              </p>
-            </description>
-            <latex-image label="img_polar_limacon4">
+                <p>
+                  Unlike the dimpled limaçon, to the left of the <m>y</m> axis, the curve flattens out,
+                  but does not bend inward.
+                </p>
+              </description>
+              <latex-image label="img_polar_limacon4">
 
-            \begin{tikzpicture}
+              \begin{tikzpicture}
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \draw [thick,firstcolor,domain=0:360,samples=80] plot ({cos(\x)*(1.3+.6*cos(\x))},{sin(\x)*(1.3+.6*cos(\x))});
+              \draw [thick,firstcolor,domain=0:360,samples=80] plot ({cos(\x)*(1.3+.6*cos(\x))},{sin(\x)*(1.3+.6*cos(\x))});
 
-            \end{tikzpicture}
+              \end{tikzpicture}
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarlimacon4.tex END -->
-        </figure>
-      </sidebyside>
-    </figure>
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarlimacon4.tex END -->
+          </figure>
+        </sidebyside>
+      </figure>
 
-    <p>
-      Symmetric about <m>x</m>-axis: <m>r=a\pm b\cos(\theta)</m>
-    </p>
-    <p>
-      Symmetric about <m>y</m>-axis: <m>r=a\pm b\sin(\theta)</m>; <m>a,b \gt 0</m>
-    </p>
+      <p>
+        Symmetric about <m>x</m>-axis: <m>r=a\pm b\cos(\theta)</m>
+      </p>
+      <p>
+        Symmetric about <m>y</m>-axis: <m>r=a\pm b\sin(\theta)</m>; <m>a,b \gt 0</m>
+      </p>
 
-    <pagebreak-latex/>
-    
-    <figure xml:id="fig_polar_roses" hstretch="450">
-      <caption>Rose curves</caption>
-      <sidebyside valign="bottom" widths="23% 23% 23% 23%">
-        <figure xml:id="fig_polar_rose1">
-          <caption><m>r=a\cos(2\theta)</m></caption>
-          <!-- START figures/fig_polarrose1.tex -->
-          <image>
-            <shortdescription>A rose curve with four leaves along the coordinate axes.</shortdescription>
-            <description>
-              <p>
-                The curve <m>r=\cos(2\theta)</m> is four-leaf rose curve; it appears to be the same as the one in <xref ref="ex_polar5"/>.
-                Two of the leaves lie along the <m>x</m> axis, and two leaves lie along the <m>y</m> axis.
-              </p>
-            </description>
-            <latex-image label="img_polar_rose1">
+      <pagebreak-latex/>
+      
+      <figure xml:id="fig_polar_roses" hstretch="450">
+        <caption>Rose curves</caption>
+        <sidebyside valign="bottom" widths="23% 23% 23% 23%">
+          <figure xml:id="fig_polar_rose1">
+            <caption><m>r=a\cos(2\theta)</m></caption>
+            <!-- START figures/fig_polarrose1.tex -->
+            <image>
+              <shortdescription>A rose curve with four leaves along the coordinate axes.</shortdescription>
+              <description>
+                <p>
+                  The curve <m>r=\cos(2\theta)</m> is four-leaf rose curve; it appears to be the same as the one in <xref ref="ex_polar5"/>.
+                  Two of the leaves lie along the <m>x</m> axis, and two leaves lie along the <m>y</m> axis.
+                </p>
+              </description>
+              <latex-image label="img_polar_rose1">
 
-            \begin{tikzpicture}
+              \begin{tikzpicture}
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \draw [thick,firstcolor,domain=0:360,samples=180] plot ({cos(\x)*(1.9*cos(2*\x))},{sin(\x)*(1.9*cos(2*\x))});
+              \draw [thick,firstcolor,domain=0:360,samples=180] plot ({cos(\x)*(1.9*cos(2*\x))},{sin(\x)*(1.9*cos(2*\x))});
 
-            \end{tikzpicture}
+              \end{tikzpicture}
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarrose1.tex END -->
-        </figure>
-        <figure xml:id="fig_polar_rose2">
-          <caption><m>r=a\sin(2\theta)</m></caption>
-          <!-- START figures/fig_polarrose2.tex -->
-          <image>
-            <shortdescription>A rose curve with four leaves, each in one of the quadrants.</shortdescription>
-            <description>
-              <p>
-                The curve <m>r=\sin(2\theta)</m> is a rose curve with four leaves.
-                It is has the same appearance as the rose curve in <xref ref="fig_polar_rose1"/>,
-                but it is rotated by 45 degrees, so that each leaf lies in one of the four quadrants.
-              </p>
-            </description>
-            <latex-image label="img_polar_rose2">
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarrose1.tex END -->
+          </figure>
+          <figure xml:id="fig_polar_rose2">
+            <caption><m>r=a\sin(2\theta)</m></caption>
+            <!-- START figures/fig_polarrose2.tex -->
+            <image>
+              <shortdescription>A rose curve with four leaves, each in one of the quadrants.</shortdescription>
+              <description>
+                <p>
+                  The curve <m>r=\sin(2\theta)</m> is a rose curve with four leaves.
+                  It is has the same appearance as the rose curve in <xref ref="fig_polar_rose1"/>,
+                  but it is rotated by 45 degrees, so that each leaf lies in one of the four quadrants.
+                </p>
+              </description>
+              <latex-image label="img_polar_rose2">
 
-            \begin{tikzpicture}
+              \begin{tikzpicture}
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \draw [thick,firstcolor,domain=0:360,samples=180] plot ({cos(\x)*(1.9*sin(2*\x))},{sin(\x)*(1.9*sin(2*\x))});
+              \draw [thick,firstcolor,domain=0:360,samples=180] plot ({cos(\x)*(1.9*sin(2*\x))},{sin(\x)*(1.9*sin(2*\x))});
 
-            \end{tikzpicture}
+              \end{tikzpicture}
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarrose2.tex END -->
-        </figure>
-        <figure xml:id="fig_polar_rose3">
-          <caption><m>r=a\cos(3\theta)</m></caption>
-          <!-- START figures/fig_polarrose4.tex -->
-          <image>
-            <shortdescription>A rose curve with three leaves, symmetric about the x axis.</shortdescription>
-            <description>
-              <p>
-                The curve <m>r=\cos(3\theta)</m> is a rose curve with three leaves.
-                The leaves are narrower in appearance than those of the four-leaf rose curves.
-              </p>
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarrose2.tex END -->
+          </figure>
+          <figure xml:id="fig_polar_rose3">
+            <caption><m>r=a\cos(3\theta)</m></caption>
+            <!-- START figures/fig_polarrose4.tex -->
+            <image>
+              <shortdescription>A rose curve with three leaves, symmetric about the x axis.</shortdescription>
+              <description>
+                <p>
+                  The curve <m>r=\cos(3\theta)</m> is a rose curve with three leaves.
+                  The leaves are narrower in appearance than those of the four-leaf rose curves.
+                </p>
 
-              <p>
-                The curve overall is symmetric about the <m>x</m> axis.
-                One leaf lies along the positive <m>x</m> axis,
-                while the other two leaves are in the second and third quadrants.
-              </p>
-            </description>
-            <latex-image label="img_polar_rose3">
+                <p>
+                  The curve overall is symmetric about the <m>x</m> axis.
+                  One leaf lies along the positive <m>x</m> axis,
+                  while the other two leaves are in the second and third quadrants.
+                </p>
+              </description>
+              <latex-image label="img_polar_rose3">
 
-            \begin{tikzpicture}
+              \begin{tikzpicture}
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \draw [thick,firstcolor,domain=0:360,samples=160] plot ({cos(\x)*(1.9*cos(3*\x))},{sin(\x)*(1.9*cos(3*\x))});
+              \draw [thick,firstcolor,domain=0:360,samples=160] plot ({cos(\x)*(1.9*cos(3*\x))},{sin(\x)*(1.9*cos(3*\x))});
 
-            \end{tikzpicture}
+              \end{tikzpicture}
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarrose4.tex END -->
-        </figure>
-        <figure xml:id="fig_polar_rose4">
-          <caption><m>r=a\sin(3\theta)</m></caption>
-          <!-- START figures/fig_polarrose3.tex -->
-          <image>
-            <shortdescription>A rose curve with three leaves, symmetric about the <m>y</m> axis.</shortdescription>
-            <description>
-              <p>
-                Another rose curve with three leaves, this time given by <m>r=\sin(3\theta)</m>.
-                The curve is symmetric about the <m>y</m>.
-                One leaf lies along the negative <m>y</m> axis,
-                while the other two leaves are in the first and second quadrants.
-              </p>
-            </description>
-            <latex-image label="img_polar_rose4">
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarrose4.tex END -->
+          </figure>
+          <figure xml:id="fig_polar_rose4">
+            <caption><m>r=a\sin(3\theta)</m></caption>
+            <!-- START figures/fig_polarrose3.tex -->
+            <image>
+              <shortdescription>A rose curve with three leaves, symmetric about the <m>y</m> axis.</shortdescription>
+              <description>
+                <p>
+                  Another rose curve with three leaves, this time given by <m>r=\sin(3\theta)</m>.
+                  The curve is symmetric about the <m>y</m>.
+                  One leaf lies along the negative <m>y</m> axis,
+                  while the other two leaves are in the first and second quadrants.
+                </p>
+              </description>
+              <latex-image label="img_polar_rose4">
 
-            \begin{tikzpicture}
+              \begin{tikzpicture}
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \draw [thick,firstcolor,domain=0:360,samples=160] plot ({cos(\x)*(1.9*sin(3*\x))},{sin(\x)*(1.9*sin(3*\x))});
+              \draw [thick,firstcolor,domain=0:360,samples=160] plot ({cos(\x)*(1.9*sin(3*\x))},{sin(\x)*(1.9*sin(3*\x))});
 
-            \end{tikzpicture}
+              \end{tikzpicture}
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarrose3.tex END -->
-        </figure>
-      </sidebyside>
-    </figure>
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarrose3.tex END -->
+          </figure>
+        </sidebyside>
+      </figure>
 
-    <p>
-      Symmetric about <m>x</m>-axis: <m>r=a \cos(n\theta)</m>
-    </p>
+      <p>
+        Symmetric about <m>x</m>-axis: <m>r=a \cos(n\theta)</m>
+      </p>
 
-    <p>
-      Symmetric about <m>y</m>-axis: <m>r=a\sin(n\theta)</m>
-    </p>
+      <p>
+        Symmetric about <m>y</m>-axis: <m>r=a\sin(n\theta)</m>
+      </p>
 
-    <p>
-      Curve contains <m>2n</m> petals when <m>n</m> is even and <m>n</m> petals when <m>n</m> is odd.
-    </p>
+      <p>
+        Curve contains <m>2n</m> petals when <m>n</m> is even and <m>n</m> petals when <m>n</m> is odd.
+      </p>
 
-    <figure xml:id="fig_polar_special" hstretch="450">
-      <caption>Special Curves</caption>
-      <sidebyside valign="bottom" widths="23% 23% 23% 23%">
-        <figure xml:id="fig_polar_special1">
-          <caption>Rose curve: <m>r=a\sin(\theta/5)</m></caption>
-          <!-- START figures/fig_polarspecial1.tex -->
-          <image>
-            <shortdescription>A polar curve consisting of three loops.</shortdescription>
-            <description>
-              <p>
-                The curve <m>r=\sin(\theta/5)</m> is also known as a rose curve,
-                but it is more similar to a limaçon in appearance,
-                except that it has more loops.
-              </p>
+      <figure xml:id="fig_polar_special" hstretch="450">
+        <caption>Special Curves</caption>
+        <sidebyside valign="bottom" widths="23% 23% 23% 23%">
+          <figure xml:id="fig_polar_special1">
+            <caption>Rose curve: <m>r=a\sin(\theta/5)</m></caption>
+            <!-- START figures/fig_polarspecial1.tex -->
+            <image>
+              <shortdescription>A polar curve consisting of three loops.</shortdescription>
+              <description>
+                <p>
+                  The curve <m>r=\sin(\theta/5)</m> is also known as a rose curve,
+                  but it is more similar to a limaçon in appearance,
+                  except that it has more loops.
+                </p>
 
-              <p>
-                The curve is symmetric about the <m>y</m> axis.
-                There are three loops in total, each of which intersects the <m>y</m> axis twice.
-                The smallest loop has a teardrop shape. It lies inside the middle loop,
-                which is heart-shaped.
-                The middle loop, in turn, lies inside of the largest loop,
-                which appears nearly circular, except that it has a slight cusp at the bottom,
-                where it joins with the middle loop.
-              </p>
-            </description>
-            <latex-image label="img_polar_special1">
+                <p>
+                  The curve is symmetric about the <m>y</m> axis.
+                  There are three loops in total, each of which intersects the <m>y</m> axis twice.
+                  The smallest loop has a teardrop shape. It lies inside the middle loop,
+                  which is heart-shaped.
+                  The middle loop, in turn, lies inside of the largest loop,
+                  which appears nearly circular, except that it has a slight cusp at the bottom,
+                  where it joins with the middle loop.
+                </p>
+              </description>
+              <latex-image label="img_polar_special1">
 
-            \begin{tikzpicture}
+              \begin{tikzpicture}
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \draw [thick,firstcolor,domain=0:900,samples=200] plot ({cos(\x)*(1.9*sin(\x/5))},{sin(\x)*(1.9*sin(\x/5))});
+              \draw [thick,firstcolor,domain=0:900,samples=200] plot ({cos(\x)*(1.9*sin(\x/5))},{sin(\x)*(1.9*sin(\x/5))});
 
-            \end{tikzpicture}
+              \end{tikzpicture}
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarspecial1.tex END -->
-        </figure>
-        <figure xml:id="fig_polar_special2">
-          <caption>Rose curve: <m>r=a\sin(2\theta/5)</m></caption>
-          <!-- START figures/fig_polarspecial2.tex -->
-          <image>
-            <shortdescription>An elaborate polar curve consisting of many intersecting loops.</shortdescription>
-            <description>
-              <p>
-                The curve <m>r=\sin(2\theta/5)</m> is also known as a rose curve,
-                but it is more elaborate than any of the earlier examples.
-              </p>
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarspecial1.tex END -->
+          </figure>
+          <figure xml:id="fig_polar_special2">
+            <caption>Rose curve: <m>r=a\sin(2\theta/5)</m></caption>
+            <!-- START figures/fig_polarspecial2.tex -->
+            <image>
+              <shortdescription>An elaborate polar curve consisting of many intersecting loops.</shortdescription>
+              <description>
+                <p>
+                  The curve <m>r=\sin(2\theta/5)</m> is also known as a rose curve,
+                  but it is more elaborate than any of the earlier examples.
+                </p>
 
-              <p>
-                The curve is symmetric about both axes, and consists of many loops of varying size.
-                These loops intesect each other several times.
-                The overall appearance is similar to a sort of braided knot.
-              </p>
-            </description>
-            <latex-image label="img_polar_special2">
+                <p>
+                  The curve is symmetric about both axes, and consists of many loops of varying size.
+                  These loops intesect each other several times.
+                  The overall appearance is similar to a sort of braided knot.
+                </p>
+              </description>
+              <latex-image label="img_polar_special2">
 
-            \begin{tikzpicture}
+              \begin{tikzpicture}
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \draw [thick,firstcolor,domain=0:1800,samples=500] plot ({cos(\x)*(1.9*cos(2*\x/5))},{sin(\x)*(1.9*cos(2*\x/5))});
+              \draw [thick,firstcolor,domain=0:1800,samples=500] plot ({cos(\x)*(1.9*cos(2*\x/5))},{sin(\x)*(1.9*cos(2*\x/5))});
 
-            \end{tikzpicture}
+              \end{tikzpicture}
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarspecial2.tex END -->
-        </figure>
-        <figure xml:id="fig_polar_special3">
-          <caption>Lemniscate: <m>r^2=a^2\cos(2\theta)</m></caption>
-          <!-- START figures/fig_polarspecial3.tex -->
-          <image>
-            <shortdescription>A lemniscate curve, which has the shape of a figure-eight.</shortdescription>
-            <description>
-              <p>
-                The lemniscate <m>r^2 = \cos^2(2\theta)</m> is a figure-eight curve.
-                Since <m>r^2</m> cannot be positive,
-                the points on the curve all correspond to angles where <m>\cos(2\theta)</m> is positive.
-                The curve is symmetric about the <m>x</m> axis, and looks much like the symbol for infinity.
-              </p>
-            </description>
-            <latex-image label="img_polar_special3">
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarspecial2.tex END -->
+          </figure>
+          <figure xml:id="fig_polar_special3">
+            <caption>Lemniscate: <m>r^2=a^2\cos(2\theta)</m></caption>
+            <!-- START figures/fig_polarspecial3.tex -->
+            <image>
+              <shortdescription>A lemniscate curve, which has the shape of a figure-eight.</shortdescription>
+              <description>
+                <p>
+                  The lemniscate <m>r^2 = \cos^2(2\theta)</m> is a figure-eight curve.
+                  Since <m>r^2</m> cannot be positive,
+                  the points on the curve all correspond to angles where <m>\cos(2\theta)</m> is positive.
+                  The curve is symmetric about the <m>x</m> axis, and looks much like the symbol for infinity.
+                </p>
+              </description>
+              <latex-image label="img_polar_special3">
 
-            \begin{tikzpicture}
+              \begin{tikzpicture}
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \draw [thick,firstcolor,domain=-45:45,samples=70] plot ({cos(\x)*(1.9*sqrt(cos(2*\x)))},{sin(\x)*(1.9*sqrt(cos(2*\x)))});
-            \draw [thick,firstcolor,domain=-45:45,samples=70] plot ({-cos(\x)*(1.9*sqrt(cos(2*\x)))},{-sin(\x)*(1.9*sqrt(cos(2*\x)))});
+              \draw [thick,firstcolor,domain=-45:45,samples=70] plot ({cos(\x)*(1.9*sqrt(cos(2*\x)))},{sin(\x)*(1.9*sqrt(cos(2*\x)))});
+              \draw [thick,firstcolor,domain=-45:45,samples=70] plot ({-cos(\x)*(1.9*sqrt(cos(2*\x)))},{-sin(\x)*(1.9*sqrt(cos(2*\x)))});
 
-            \end{tikzpicture}
+              \end{tikzpicture}
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarspecial3.tex END -->
-        </figure>
-        <figure xml:id="fig_polar_special4">
-          <caption>Eight Curve: <m>r^2=a^2\sec^4(\theta) \cos(2\theta)</m></caption>
-          <!-- START figures/fig_polarspecial4.tex -->
-          <image>
-            <shortdescription>A polar curve in the shape of a figure-eight.</shortdescription>
-            <description>
-              <p>
-                This final curve in the gallery is also a figure-eight curve.
-                Like the lemniscate, it is symmetric about the <m>x</m> axis,
-                but it is flatter at the ends than the lemniscate.
-              </p>
-            </description>
-            <latex-image label="img_polar_special4">
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarspecial3.tex END -->
+          </figure>
+          <figure xml:id="fig_polar_special4">
+            <caption>Eight Curve: <m>r^2=a^2\sec^4(\theta) \cos(2\theta)</m></caption>
+            <!-- START figures/fig_polarspecial4.tex -->
+            <image>
+              <shortdescription>A polar curve in the shape of a figure-eight.</shortdescription>
+              <description>
+                <p>
+                  This final curve in the gallery is also a figure-eight curve.
+                  Like the lemniscate, it is symmetric about the <m>x</m> axis,
+                  but it is flatter at the ends than the lemniscate.
+                </p>
+              </description>
+              <latex-image label="img_polar_special4">
 
-            \begin{tikzpicture}
+              \begin{tikzpicture}
 
-            \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
-            \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
+              \draw [&lt;-&gt;] (-2.1,0) -- (2.1,0);
+              \draw [&lt;-&gt;] (0,-2.1) -- (0,2.1);
 
-            \draw [thick,firstcolor,domain=-45:45,samples=80] plot ({cos(\x)*(1.9*sqrt(sec(\x)^4*cos(2*\x)))},{sin(\x)*(1.9*sqrt(sec(\x)^4*cos(2*\x)))});
-            \draw [thick,firstcolor,domain=-45:45,samples=80] plot ({-cos(\x)*(1.9*sqrt(sec(\x)^4*cos(2*\x)))},{-sin(\x)*(1.9*sqrt(sec(\x)^4*cos(2*\x)))});
+              \draw [thick,firstcolor,domain=-45:45,samples=80] plot ({cos(\x)*(1.9*sqrt(sec(\x)^4*cos(2*\x)))},{sin(\x)*(1.9*sqrt(sec(\x)^4*cos(2*\x)))});
+              \draw [thick,firstcolor,domain=-45:45,samples=80] plot ({-cos(\x)*(1.9*sqrt(sec(\x)^4*cos(2*\x)))},{-sin(\x)*(1.9*sqrt(sec(\x)^4*cos(2*\x)))});
 
-            \end{tikzpicture}
+              \end{tikzpicture}
 
-            </latex-image>
-          </image>
-          <!-- figures/fig_polarspecial4.tex END -->
-        </figure>
-      </sidebyside>
-    </figure>
+              </latex-image>
+            </image>
+            <!-- figures/fig_polarspecial4.tex END -->
+          </figure>
+        </sidebyside>
+      </figure>
+    </paragraphs>
 
     <p>
       Earlier we discussed how each point in the plane does not have a unique representation in polar form.
diff --git a/ptx/sec_sequences.ptx b/ptx/sec_sequences.ptx
index 22f3c36d1..b20b8e088 100644
--- a/ptx/sec_sequences.ptx
+++ b/ptx/sec_sequences.ptx
@@ -153,7 +153,7 @@
               and the values of the terms are plotted on the vertical axis.
               To visualize this sequence, see <xref ref="fig_seq1a"/>.
             </p>
-            <figure xml:id="fig_seq1a" vshift="8">
+            <figure xml:id="fig_seq1a" vshift="5">
               <caption>Plotting the sequence in <xref ref="item_ex_seq1_1"/></caption>
         <!-- START figures/fig_seq1a.tex -->
               <image width="47%">
@@ -205,7 +205,7 @@
               consisting of only the values 3 and 5.
               This sequence is plotted in <xref ref="fig_seq1b"/>.
             </p>
-            <figure xml:id="fig_seq1b" vshift="-1">
+            <figure xml:id="fig_seq1b" vshift="0">
               <caption>Plotting the sequence in <xref ref="item_ex_seq1_2"/></caption>
         <!-- START figures/fig_seq1b.tex -->
               <image width="47%">
@@ -262,7 +262,7 @@
               due to the fact that the exponent of <m>-1</m> is a special quadratic.
               This sequence is plotted in <xref ref="fig_seq1c"/>.
             </p>
-            <figure xml:id="fig_seq1c" vshift="-3">
+            <figure xml:id="fig_seq1c" vshift="-2">
               <caption>Plotting the sequence in <xref ref="item_ex_seq1_3"/></caption>
         <!-- START figures/fig_seq1c.tex -->
               <image width="47%">
@@ -644,7 +644,7 @@
                 xlabel={$n$}
                 ]
 
-                \addplot [only marks,firstcolor,mark size={.75pt},domain=1:100,samples=21] {(3*x^2 - 2*x + 1)/(x^2 - 1000)};
+                \addplot [only marks,firstcolor,mark size={1.75pt},domain=1:100,samples=21] {(3*x^2 - 2*x + 1)/(x^2 - 1000)};
 
                 \draw (axis cs:60,-8) node { $\ds a_n = \frac{3n^2 - 2n + 1}{n^2 - 1000}$};
 
@@ -705,7 +705,7 @@
                 xlabel={$n$}
                 ]
 
-                \addplot [only marks,firstcolor,mark size={.75pt},domain=1:100,samples=101] {cos(deg(x))};
+                \addplot [only marks,firstcolor,mark size={1.5pt},domain=1:100,samples=101] {cos(deg(x))};
 
                 \end{axis}
 
@@ -777,7 +777,7 @@
                 xlabel={$n$}
                 ]
 
-                \addplot [only marks,firstcolor,mark size={.75pt},domain=1:20,samples=20] {((-1)^x)/x};
+                \addplot [only marks,firstcolor,mark size={1.75pt},domain=1:20,samples=20] {((-1)^x)/x};
 
                 \draw (axis cs:10,-.7) node { $\ds a_n = \frac{(-1)^n}{n}$};
 
diff --git a/ptx/sec_series.ptx b/ptx/sec_series.ptx
index 239d11e78..4232ddaea 100644
--- a/ptx/sec_series.ptx
+++ b/ptx/sec_series.ptx
@@ -546,7 +546,7 @@
                 </md>.
                 This is illustrated in <xref ref="fig_series2a"/>.
               </p>
-              <figure xml:id="fig_series2a" vshift="12">
+              <figure xml:id="fig_series2a" vshift="7">
                 <caption>Scatter plots for the series in <xref ref="item_ex_ser2_1"/></caption>
             <!-- START figures/fig_series2a.tex -->
                 <image width="47%">
@@ -608,7 +608,7 @@
                 The partial sums of this series are plotted in <xref ref="fig_series2b"/>.
                 Note how the partial sums are not purely increasing as some of the terms of the sequence <m>\{(-1/2)^n\}</m> are negative.
               </p>
-              <figure xml:id="fig_series2b" vshift="3.5">
+              <figure xml:id="fig_series2b" vshift="4.5">
                 <caption>Scatter plots for the series in <xref ref="item_ex_ser2_2"/></caption>
           <!-- START figures/fig_series2b.tex -->
                 <image width="47%">
@@ -670,7 +670,7 @@
                 to diverge.)
                 This is illustrated in <xref ref="fig_series2c"/>.
               </p>
-              <figure xml:id="fig_series2c" vshift="0">
+              <figure xml:id="fig_series2c" vshift="1">
                 <caption>Scatter plots for the series in <xref ref="item_ex_ser2_3"/></caption>
           <!-- START figures/fig_series2c.tex -->
                 <image width="47%">
@@ -725,6 +725,8 @@
     </example>
   </subsection>
 
+  <pagebreak-latex/>
+
   <subsection>
     <title><m>p</m>-Series</title>
     <p>
@@ -912,7 +914,7 @@
       </solution>
     </example>
 
-        <exercise label="APEX-PROTEUS-series-3-v1">
+        <exercise label="APEX-PROTEUS-series-3-v1" component="proteus">
       <title>PROTEUS EXERCISE</title>
       
       <statement>
diff --git a/ptx/sec_space_coord.ptx b/ptx/sec_space_coord.ptx
index e43e68e06..08e9a6a42 100644
--- a/ptx/sec_space_coord.ptx
+++ b/ptx/sec_space_coord.ptx
@@ -614,7 +614,7 @@
       shown in <xref ref="fig_space2"/>.
     </p>
 
-    <figure xml:id="fig_space2" vshift="1">
+    <figure xml:id="fig_space2" vshift="3">
       <caption>The plane <m>x=2</m></caption>
       <!-- START figures/figspace2_3D.asy -->
       <image width="47%">
@@ -684,7 +684,7 @@
           and is bounded by planes in the <m>y</m> direction.
         </p>
 
-        <figure xml:id="fig_space3" vshift="-5">
+        <figure xml:id="fig_space3" vshift="-1">
           <caption>Sketching the boundaries of a region in <xref ref="ex_space3"/></caption>
           <!-- START figures/figspace3_3D.asy -->
           <image width="47%">
diff --git a/ptx/sec_vector_intro.ptx b/ptx/sec_vector_intro.ptx
index 1aa4f651c..c1110180e 100644
--- a/ptx/sec_vector_intro.ptx
+++ b/ptx/sec_vector_intro.ptx
@@ -534,7 +534,7 @@
         </md>.
       </p>
 
-      <figure xml:id="fig_vect2" vshift="-2">
+      <figure xml:id="fig_vect2" vshift="0">
         <caption>Graphing the sum of vectors in <xref ref="ex_vect2"/></caption>
         <!-- START figures/fig_vect2.tex -->
         <image width="47%">
@@ -616,7 +616,7 @@
         <idx><h>vectors</h><h>zero vector</h></idx>
   </p>
 
-  <figure xml:id="fig_vect2b" vshift="0">
+  <figure xml:id="fig_vect2b" vshift="-1">
     <caption>Illustrating how to add vectors using the Head to Tail Rule and Parallelogram Law</caption>
     <!-- START figures/fig_vect2b.tex -->
     <image width="47%">
@@ -716,7 +716,7 @@
         </md>.
       </p>
 
-      <figure xml:id="fig_vect4" vshift="4">
+      <figure xml:id="fig_vect4" vshift="2">
         <caption>Illustrating how to subtract vectors graphically</caption>
         <!-- START figures/fig_vect4.tex -->
         <image width="47%">
@@ -808,7 +808,7 @@
               </md>.
             </p>
 
-            <figure xml:id="fig_vect3" vshift="-1">
+            <figure xml:id="fig_vect3" vshift="0">
               <caption>Graphing vectors <m>\vec v</m> and <m>2\vec v</m> in <xref ref="ex_vect3"/></caption>
             <!-- START figures/fig_vect3.tex -->
               <image width="47%">
@@ -1196,7 +1196,7 @@
     <m>\vec v_2</m> are parallel if there is a scalar <m>c\neq 0</m> such that <m>\vec v_1 = c\vec v_2</m>
     (see marginal note).
   </p>
-  <aside xml:id="aside-def-orthogonal" vshift="0">
+  <aside xml:id="aside-def-orthogonal" vshift="-1">
     <title>Direction and the zero vector</title>
 
     <p>
diff --git a/ptx/sec_vvf_calc.ptx b/ptx/sec_vvf_calc.ptx
index e06038672..28390e083 100644
--- a/ptx/sec_vvf_calc.ptx
+++ b/ptx/sec_vvf_calc.ptx
@@ -700,7 +700,7 @@
           Thus <m>\vrp(-1) = \la 1,-2,3\ra</m>.
         </p>
 
-        <figure xml:id="fig_vvfderiv1" vshift="1">
+        <figure xml:id="fig_vvfderiv1" vshift="-1">
           <caption>Graphing a curve in space with its tangent line</caption>
 
           <!-- START figures/figvvfderiv1_3D.asy -->
diff --git a/ptx/sec_vvf_motion.ptx b/ptx/sec_vvf_motion.ptx
index cf090c1d9..497d87e1a 100644
--- a/ptx/sec_vvf_motion.ptx
+++ b/ptx/sec_vvf_motion.ptx
@@ -1141,7 +1141,7 @@
                 We can compute average speed by dividing: <m>12.88/4 = 3.22\,\text{m/s}</m>.
               </p>
 
-              <figure xml:id="fig_motion6" vshift="-4">
+              <figure xml:id="fig_motion6" vshift="-1">
                 <caption>The path of the particle in <xref ref="ex_motion6"/></caption>
 
               <!-- START figures/figmotion6_3D.asy -->

From ae72cffcd6b6d3505ad213ec41ddace938b450e4 Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Tue, 2 Jun 2026 16:37:40 -0600
Subject: [PATCH 03/18] other layout adjustments

---
 ptx/sec_FTC.ptx                   |  4 +++-
 ptx/sec_antider.ptx               |  2 +-
 ptx/sec_cylindrical_spherical.ptx |  9 +++++----
 ptx/sec_deriv_intro.ptx           |  2 ++
 ptx/sec_disk.ptx                  |  6 ++++--
 ptx/sec_dot_product.ptx           | 20 ++++++++++----------
 ptx/sec_graph_concavity.ptx       | 16 ++++++++++------
 ptx/sec_multi_limit.ptx           | 13 +++++++------
 ptx/sec_numerical_integration.ptx | 20 ++++++++++----------
 ptx/sec_shell_method.ptx          |  2 ++
 ptx/sec_total_differential.ptx    |  2 +-
 ptx/sec_trig_sub.ptx              | 11 ++++++++---
 ptx/sec_trigint.ptx               |  7 +++----
 ptx/sec_triple_int.ptx            |  2 ++
 ptx/sec_vector_fields.ptx         |  7 +++++--
 15 files changed, 73 insertions(+), 50 deletions(-)

diff --git a/ptx/sec_FTC.ptx b/ptx/sec_FTC.ptx
index ac0bc10bb..ac8f0ccb2 100644
--- a/ptx/sec_FTC.ptx
+++ b/ptx/sec_FTC.ptx
@@ -1039,6 +1039,8 @@
       Let's practice this once more.
     </p>
 
+    <enlarge-page skipsize="2"/>
+
     <example xml:id="ex_ftc12">
       <title>The FTC, Part 1, and the Chain Rule</title>
       <statement>
@@ -1542,7 +1544,7 @@
       we leave it to the reader to see how.
     </p>
 
-    <aside vshift="0">
+    <aside vshift="1">
       <p>
         <xref ref="thm_mvt2"/>
         simply says that there is a rectangle with height <m>f(c)</m> and width <m>b-a</m>,
diff --git a/ptx/sec_antider.ptx b/ptx/sec_antider.ptx
index a4a5beb63..898b13852 100644
--- a/ptx/sec_antider.ptx
+++ b/ptx/sec_antider.ptx
@@ -378,7 +378,7 @@
       as we learn.
     </p>
 
-    <theorem xml:id="thm_indef_alg" hstretch="360" hskip="60">
+    <theorem xml:id="thm_indef_alg" hstretch="360" hskip="70">
       <title>Derivatives and Antiderivatives</title>
       <statement>
         <p>
diff --git a/ptx/sec_cylindrical_spherical.ptx b/ptx/sec_cylindrical_spherical.ptx
index 504c9f603..83b9ce403 100644
--- a/ptx/sec_cylindrical_spherical.ptx
+++ b/ptx/sec_cylindrical_spherical.ptx
@@ -927,7 +927,8 @@
       The following Key Idea gives conversions to/from our three spatial coordinate systems.
     </p>
 
-    <insight xml:id="idea_convert_coords" hstretch="330" hskip="60">
+    <!-- <insight xml:id="idea_convert_coords" hstretch="330" hskip="60"> -->
+    <insight xml:id="idea_convert_coords" hstretch="330">
       <title>Converting Between Rectangular, Cylindrical and Spherical Coordinates</title>
       <p>
         <ul>
@@ -1037,7 +1038,7 @@
           with the positive <m>z</m>-axis its axis of symmetry, with point at the origin.
         </p>
 
-        <figure xml:id="fig_spherical1" vshift="1">
+        <figure xml:id="fig_spherical1" vshift="-1">
           <caption>Graphing the canonical surfaces in spherical coordinates from <xref ref="ex_spherical1"/></caption>
           <image width="47%">
             <shortdescription>A three-dimensional plot showing three surfaces, each of which is obtained by fixing a value of one of the three spherical coordinates.</shortdescription>
@@ -1197,7 +1198,7 @@
       </md>.
     </p>
 
-    <figure xml:id="fig_sphericalwedge" vshift="-2">
+    <figure xml:id="fig_sphericalwedge" vshift="-3">
       <caption>Approximating the volume of a standard region in space using spherical coordinates</caption>
       <image width="47%">
         <shortdescription>A schematic diagram illustrating how the spherical volume element is computed.</shortdescription>
@@ -1412,7 +1413,7 @@
       Again, this development of <m>dV</m> should sound reasonable,
       and the following theorem states it is the appropriate manner by which triple integrals are to be evaluated in spherical coordinates.
     </p>
-    <aside vshift="-6">
+    <aside vshift="-7">
       <p>
         It is generally most intuitive to evaluate the triple integral in <xref ref="thm_triple_int_spherical"/>
         by integrating with respect to <m>\rho</m> first;
diff --git a/ptx/sec_deriv_intro.ptx b/ptx/sec_deriv_intro.ptx
index 207d1ce56..94e5dcad8 100644
--- a/ptx/sec_deriv_intro.ptx
+++ b/ptx/sec_deriv_intro.ptx
@@ -966,6 +966,8 @@
       Examples will help us understand this definition.
     </p>
 
+    <enlarge-page skipsize="2"/>
+
     <example xml:id="ex_deriv1">
       <title>Finding the derivative of a function</title>
       <statement>
diff --git a/ptx/sec_disk.ptx b/ptx/sec_disk.ptx
index 96aa429ba..03df53791 100644
--- a/ptx/sec_disk.ptx
+++ b/ptx/sec_disk.ptx
@@ -272,7 +272,9 @@
         the volume of this slice would then be about <m>36\Delta x_i</m> <quantity><mag/><unit base="inch" exp="3"/></quantity>.
       </p>
 
-      <figure xml:id="fig_disk0a" vshift="-2">
+      <pagebreak-latex/>
+      
+      <figure xml:id="fig_disk0a" vshift="-2.5">
         <caption>Cutting a slice in the pyramid in <xref ref="ex_disk0"/> at <m>x=3</m></caption>
 
         <!-- START figures/figcross_area1a_3D.asy -->
@@ -1398,7 +1400,7 @@
     Each cross section of this solid will be a washer (a disk with a hole in the center) as sketched in <xref ref="fig_washeridea2_3D"/>. This leads us to the Washer Method.
   </p>
 
-  <figure xml:id="fig_washeridea2_3D" vshift="0">
+  <figure xml:id="fig_washeridea2_3D" vshift="-0.5">
     <caption>Establishing the Washer Method; see also <xref ref="fig_washeridea1"/></caption>
 
     <!-- START figures/figwasher_idea_c_3D.asy -->
diff --git a/ptx/sec_dot_product.ptx b/ptx/sec_dot_product.ptx
index 894350376..e6073033e 100644
--- a/ptx/sec_dot_product.ptx
+++ b/ptx/sec_dot_product.ptx
@@ -1249,6 +1249,15 @@
       This use of the dot product will be very useful in future sections.
     </p>
 
+    <p>
+      Now consider <xref ref="fig_dotpprojc"/>
+      where the concept of the orthogonal projection is again illustrated.
+      It is clear that
+      <md number="yes" xml:id="eq_orthogproj">
+        \vec u = \proj uv + \vec z
+      </md>.
+    </p>
+
     <figure xml:id="fig_dotpprojc" vshift="0">
       <caption>Illustrating the orthogonal projection</caption>
       <!-- START figures/fig_dotpprojc.tex -->
@@ -1284,16 +1293,7 @@
       </image>
       <!-- figures/fig_dotpprojc.tex END -->
     </figure>
-
-    <p>
-      Now consider <xref ref="fig_dotpprojc"/>
-      where the concept of the orthogonal projection is again illustrated.
-      It is clear that
-      <md number="yes" xml:id="eq_orthogproj">
-        \vec u = \proj uv + \vec z
-      </md>.
-    </p>
-
+    
     <p>
       As we know what <m>\vec u</m> and <m>\proj uv</m> are,
       we can solve for <m>\vec z</m> and state that
diff --git a/ptx/sec_graph_concavity.ptx b/ptx/sec_graph_concavity.ptx
index 4075d1056..d90218830 100644
--- a/ptx/sec_graph_concavity.ptx
+++ b/ptx/sec_graph_concavity.ptx
@@ -995,11 +995,9 @@
           The sales of a certain product over a three-year span are modeled by <m>S(t)= t^4-8t^2+20</m>,
           where <m>t</m> is the time in years,
           shown in <xref ref="fig_conc3"/>.
-          Over the first two years, sales are decreasing.
-          Find the point at which sales are decreasing at their greatest rate.
         </p>
-        <pagebreak-latex/>
-        <figure xml:id="fig_conc3" vshift="1.5">
+
+        <figure xml:id="fig_conc3" vshift="2">
           <caption>A graph of <m>S(t)</m> in <xref ref="ex_conc3"/>, modeling the sale of a product over time</caption>
           <!-- START figures/fig_conc3.tex -->
           <image width="47%">
@@ -1029,6 +1027,12 @@
           </image>
           <!-- figures/fig_conc3.tex END -->
         </figure>
+
+        <p>
+          Over the first two years, sales are decreasing.
+          Find the point at which sales are decreasing at their greatest rate.
+        </p>
+        <!-- <pagebreak-latex/> -->
       </statement>
       <solution>
         <p>
@@ -1061,7 +1065,7 @@
           so the decline in sales is <q>leveling off.</q>
         </p>
 
-        <figure xml:id="fig_conc3b" vshift="2.5">
+        <figure xml:id="fig_conc3b" vshift="3">
           <caption>A graph of <m>S(t)</m> in <xref ref="ex_conc3"/>, along with <m>S'(t)</m></caption>
           <!-- START figures/fig_conc3b.tex -->
           <image width="47%">
@@ -1156,7 +1160,7 @@
       See <xref ref="fig_concavity6"/> for a visualization of this.
     </p>
 
-    <figure xml:id="fig_concavity6" vshift="-4">
+    <figure xml:id="fig_concavity6" vshift="-4.5">
       <caption>Demonstrating the fact that relative maxima occur when the graph is concave down and relative minima occur when the graph is concave up</caption>
       <!-- START figures/fig_concavity6.tex -->
       <image width="47%">
diff --git a/ptx/sec_multi_limit.ptx b/ptx/sec_multi_limit.ptx
index 2b950876b..69ca44907 100644
--- a/ptx/sec_multi_limit.ptx
+++ b/ptx/sec_multi_limit.ptx
@@ -393,11 +393,6 @@
       then <m>f(x,y)</m> should be within <m>\varepsilon</m> of <m>L</m>.
     </p>
 
-    <p>
-      Computing limits using this definition is rather cumbersome.
-      The following theorem allows us to evaluate limits much more easily.
-    </p>
-
     <figure xml:id="fig_multilimitdef" vshift="2">
       <caption><em>Illustrating the definition of a limit.</em> The open disk in the <m>xy</m>-plane has radius <m>\delta</m>. Let <m>(x,y)</m> be any point in this disk; <m>f(x,y)</m> is within <m>\varepsilon</m> of <m>L</m>.</caption>
 
@@ -500,6 +495,11 @@
       <!-- figures/figmultilimit_def_3D.asy END -->
     </figure>
 
+    <p>
+      Computing limits using this definition is rather cumbersome.
+      The following theorem allows us to evaluate limits much more easily.
+    </p>
+
     <theorem xml:id="thm_multi_limit_algebra">
       <title>Basic Limit Properties of Functions of Two Variables</title>
       <statement>
@@ -717,7 +717,8 @@
                 Now apply L'Hospital's Rule twice:
                 <md>
                   <mrow>\amp = \lim_{x\to 0}\frac{\cos\big(-x\sin(x) \big)(-\sin(x) -x\cos(x) )}{1-\cos(x) } \quad \left(0/0\right)</mrow>
-                  <mrow>\amp = \lim_{x\to 0}\frac{-\sin\big(-x\sin(x) \big)(-\sin(x) -x\cos(x) )^2+\cos\big(-x\sin(x) \big)(-2\cos(x) +x\sin(x) )}{\sin(x) }</mrow>
+                  <mrow>\amp = \lim_{x\to 0}\frac{\begin{matrix}-\sin\big(-x\sin(x) \big)(-\sin(x) -x\cos(x) )^2\phantom{\cos(x)}\\ 
+                    \phantom{\cos(x)}+\cos\big(-x\sin(x) \big)(-2\cos(x) +x\sin(x) )\end{matrix}}{\sin(x) }</mrow>
                   <!-- <mrow>\amp = \text{ <q>2/0</q> }  \Rightarrow \text{ the limit does not exist. }</mrow> -->
                 </md>.
                 This last limit is of the form <q><m>2/0</m></q>,
diff --git a/ptx/sec_numerical_integration.ptx b/ptx/sec_numerical_integration.ptx
index 89db8e1e4..880b7448e 100644
--- a/ptx/sec_numerical_integration.ptx
+++ b/ptx/sec_numerical_integration.ptx
@@ -986,61 +986,61 @@
             </row>
             <row>
               <cell><m>\overline{x_1}</m></cell>
-              <cell><m>-17\pi/80</m></cell>
+              <cell><m>-\frac{17\pi}{80}</m></cell>
               <cell><m>-0.6676</m></cell>
               <cell><m>-0.2932</m></cell>
             </row>
             <row>
               <cell><m>\overline{x_2}</m></cell>
-              <cell><m>-11 \pi/80</m></cell>
+              <cell><m>-\frac{11 \pi}{80}</m></cell>
               <cell><m>-0.4320</m></cell>
               <cell><m>-0.0805</m></cell>
             </row>
             <row>
               <cell><m>\overline{x_3}</m></cell>
-              <cell><m>-5{\pi }/{80}</m></cell>
+              <cell><m>-\frac{5\pi }{80}</m></cell>
               <cell><m>-0.1963</m></cell>
               <cell><m>-0.0076</m></cell>
             </row>
             <row>
               <cell><m>\overline{x_4}</m></cell>
-              <cell><m>1{\pi }/{80}</m></cell>
+              <cell><m>\frac{\pi }{80}</m></cell>
               <cell><m>-0.0393</m></cell>
               <cell><m>0.0001</m></cell>
             </row>
             <row>
               <cell><m>\overline{x_5}</m></cell>
-              <cell><m>7{\pi }/{80}</m></cell>
+              <cell><m>\frac{7\pi }{80}</m></cell>
               <cell><m>0.2749</m></cell>
               <cell><m>0.0208</m></cell>
             </row>
             <row>
               <cell><m>\overline{x_6}</m></cell>
-              <cell><m>{13\pi }/{80}</m></cell>
+              <cell><m>\frac{13\pi }{80}</m></cell>
               <cell><m>0.5105</m></cell>
               <cell><m>0.1327</m></cell>
             </row>
             <row>
               <cell><m>\overline{x_7}</m></cell>
-              <cell><m>{19\pi }/{80}</m></cell>
+              <cell><m>\frac{19\pi}{80}</m></cell>
               <cell><m>0.7461</m></cell>
               <cell><m>0.4035</m></cell>
             </row>
             <row>
               <cell><m>\overline{x_8}</m></cell>
-              <cell><m>{25 \pi }/{80}</m></cell>
+              <cell><m>\frac{25 \pi}{80}</m></cell>
               <cell><m>0.9817</m></cell>
               <cell><m>0.8112</m></cell>
             </row>
             <row>
               <cell><m>\overline{x_9}</m></cell>
-              <cell><m>{31 \pi }/{80}</m></cell>
+              <cell><m>\frac{31 \pi}{80}</m></cell>
               <cell><m>1.2174</m></cell>
               <cell><m>0.9729</m></cell>
             </row>
             <row>
               <cell><m>\overline{x_{10}}</m></cell>
-              <cell><m>{37 \pi }/{80}</m></cell>
+              <cell><m>\frac{37 \pi}{80}</m></cell>
               <cell><m>1.4530</m></cell>
               <cell><m>0.0740</m></cell>
             </row>
diff --git a/ptx/sec_shell_method.ptx b/ptx/sec_shell_method.ptx
index 56dafdb9f..2b08f0897 100644
--- a/ptx/sec_shell_method.ptx
+++ b/ptx/sec_shell_method.ptx
@@ -1440,6 +1440,8 @@
     We end this section with a table summarizing the usage of the Washer and Shell Methods.
   </p>
 
+  <pagebreak-latex/>
+
   <insight xml:id="idea_shell_and_washer">
     <title>Summary of the Washer and Shell Methods</title>
     <p>
diff --git a/ptx/sec_total_differential.ptx b/ptx/sec_total_differential.ptx
index 901a7c8ca..e62fc51e6 100644
--- a/ptx/sec_total_differential.ptx
+++ b/ptx/sec_total_differential.ptx
@@ -1049,7 +1049,7 @@
                   Is the measurement of the length of <m>\ell</m> more sensitive to errors in the measurement of <m>x</m> or in <m>\theta</m>?
                 </p>
 
-                <image>
+                <image width="60%">
                   <shortdescription>A right-angled triangle illustrating a wall of unknown height, a horizontal distance, and an angle.</shortdescription>
                   <description>
                     <p>
diff --git a/ptx/sec_trig_sub.ptx b/ptx/sec_trig_sub.ptx
index 99db1a367..37173eb05 100644
--- a/ptx/sec_trig_sub.ptx
+++ b/ptx/sec_trig_sub.ptx
@@ -556,7 +556,7 @@
         then make the substitution <m>u=x+3</m>,
         followed by the trigonometric substitution of <m>u=\tan(\theta)</m>:
         <md>
-          <mrow>\int \frac1{(x^2+6x+10)^2}\, dx =\int \frac1{\big((x+3)^2+1\big)^2}\, dx\amp = \int \frac1{(u^2+1)^2}\,du.</mrow>
+          <mrow>\int \frac1{(x^2+6x+10)^2}\, dx \amp =\int \frac1{\big((x+3)^2+1\big)^2}\, dx = \int \frac1{(u^2+1)^2}\,du.</mrow>
           <intertext>Now make the substitution <m>u=\tan(\theta)</m>, <m>du=\sec^2(\theta) \, d\theta</m>:</intertext>
           <mrow>\amp =	\int \frac1{(\tan^2(\theta) +1)^2}\sec^2(\theta) \, d\theta</mrow>
           <mrow>\amp = \int\frac 1{(\sec^2(\theta) )^2}\sec^2(\theta) \, d\theta</mrow>
@@ -755,7 +755,7 @@
           <statement>
             <p>
               Trigonometric Substitution works on the same principles as Integration by Substitution,
-              though it can feel <q><fillin answer="backward" width="20"/></q>.
+              though it can feel <fillin answer="backward" width="20"/>.
             </p>
           </statement>
           <evaluation>
@@ -780,7 +780,10 @@
           <statement>
             <p>
               If one uses Trigonometric Substitution on an integrand containing <m><var name="$integrand"/></m>,
-              then one should set <m>x={}</m><var name="$answer" width="20"/>.
+              then one should set <m>x</m> equal to what?
+            </p>
+            <p>
+              <var name="$answer" width="20"/>
             </p>
           </statement>
         </webwork>
@@ -1335,6 +1338,8 @@
         </exercise>
       </exercisegroup>
 
+      <enlarge-page skipsize="2"/>
+      
       <exercisegroup cols="2" xml:id="exset-trig-sub-definite">
         <introduction>
           <p>
diff --git a/ptx/sec_trigint.ptx b/ptx/sec_trigint.ptx
index 235b654d1..0c84af962 100644
--- a/ptx/sec_trigint.ptx
+++ b/ptx/sec_trigint.ptx
@@ -253,9 +253,8 @@
       The powerful program <em>Mathematica</em><trademark/> integrates
       <m>\int \sin^5(x) \cos^9(x) \, dx</m> as
       <md>
-        f(x)=-\frac{45 \cos(2 x)}{16384}-\frac{5 \cos(4 x)}{8192}+\frac{19 \cos(6
-        x)}{49152}+\frac{\cos(8 x)}{4096}-\frac{\cos(10 x)}{81920}-\frac{\cos(12
-        x)}{24576}-\frac{\cos(14 x)}{114688}
+        <mrow>f(x) =\amp -\frac{45 \cos(2 x)}{16384}-\frac{5 \cos(4 x)}{8192}+\frac{19 \cos(6x)}{49152}</mrow>
+        <mrow>\amp+\frac{\cos(8 x)}{4096}-\frac{\cos(10 x)}{81920}-\frac{\cos(12x)}{24576}-\frac{\cos(14 x)}{114688}</mrow>
       </md>,
       which clearly has a different form than our answer in
       <xref ref="ex_trigint2"/>, which is
@@ -592,7 +591,7 @@
       This strategy is outlined in the following Key Idea.
     </p>
 
-    <insight xml:id="idea_trig_int_2" hstretch="330">
+    <insight xml:id="idea_trig_int_2" hstretch="310">
       <title>Integrals Involving Powers of Tangent and Secant</title>
       <p>
         Consider <m>\ds\int\tan^m(x) \sec^n(x) \, dx</m>,
diff --git a/ptx/sec_triple_int.ptx b/ptx/sec_triple_int.ptx
index a8c4305ef..00c3a8ddd 100644
--- a/ptx/sec_triple_int.ptx
+++ b/ptx/sec_triple_int.ptx
@@ -2875,6 +2875,8 @@
       This leads us to a definition, followed by an example.
     </p>
 
+    <pagebreak-latex/>
+    
     <definition xml:id="def_triple_integral_2" hstretch="360">
       <title>Iterated Integration, (Part II)</title>
       <statement>
diff --git a/ptx/sec_vector_fields.ptx b/ptx/sec_vector_fields.ptx
index e6d1714b0..fe8c15882 100644
--- a/ptx/sec_vector_fields.ptx
+++ b/ptx/sec_vector_fields.ptx
@@ -643,8 +643,9 @@
 
     <p>
       We can also compute their cross products:
-      <md hskip="30" minisize="360">
-        <mrow>{\nabla\times \vec F }\amp = {\left\langle \frac{\partial}{\partial y}\big(x^2\big)-\frac{\partial}{\partial z}\big(y^2+z\big),\frac{\partial}{\partial z}\big(x+\sin(y)\big)-\frac{\partial}{\partial x}\big(x^2\big),\frac{\partial}{\partial x}\big(y^2+z\big)-\frac{\partial}{\partial y}\big(x+\sin(y)\big)\right\rangle }</mrow>
+      <md>
+        <mrow>\nabla\times \vec F \amp = \left\langle \frac{\partial}{\partial y}\big(x^2\big)-\frac{\partial}{\partial z}\big(y^2+z\big),\frac{\partial}{\partial z}\big(x+\sin(y)\big)-\frac{\partial}{\partial x}\big(x^2\big),\right.</mrow>
+        <mrow>\amp \phantom{=\frac{\partial}{\partial y}\big(x^2\big)-\frac{\partial}{\partial z}\big(y^2+z\big)}\left.\frac{\partial}{\partial x}\big(y^2+z\big)-\frac{\partial}{\partial y}\big(x+\sin(y)\big)\right\rangle </mrow>
         <mrow>\amp =\langle -1,-2x,-\cos(y)\rangle</mrow>
       </md>.
     </p>
@@ -1672,6 +1673,8 @@
       </solution>
     </example>
 
+    <enlarge-page skipsize="2"/>
+
     <p>
       There are some important concepts visited in this section that will be revisited in subsequent sections and again at the very end of this chapter.
       One is: given a vector field <m>\vec F</m>,

From c16201674b587f62e9bcd7a281410206f35b6e7b Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Tue, 2 Jun 2026 16:38:57 -0600
Subject: [PATCH 04/18] some exercisses need web and print versions

---
 ptx/sec_curvature.ptx                         | 19 ++++++++++++++-----
 ptx/sec_deriv_basic_rules.ptx                 |  4 ++--
 ptx/sec_deriv_prodquot.ptx                    |  4 ++--
 ptx/sec_double_int_polar.ptx                  |  3 +--
 ptx/sec_multi_chain.ptx                       | 19 ++++++++++++++++++-
 publication/publication-accelerated-print.ptx |  2 +-
 publication/publication-accelerated.ptx       |  2 +-
 .../publication-color-print-novideo.ptx       |  2 +-
 publication/publication-color-print.ptx       |  2 +-
 publication/publication-novid-print.ptx       |  2 +-
 publication/publication-print.ptx             |  2 +-
 publication/publication-standard-print.ptx    |  2 +-
 publication/publication-standard.ptx          |  2 +-
 13 files changed, 45 insertions(+), 20 deletions(-)

diff --git a/ptx/sec_curvature.ptx b/ptx/sec_curvature.ptx
index 71f96937f..47c9c6422 100644
--- a/ptx/sec_curvature.ptx
+++ b/ptx/sec_curvature.ptx
@@ -1241,10 +1241,7 @@
         <!--</webwork>-->
       </exercise>
 
-      <exercise label="TaC-curvature-5" language="math">
-        <!--<webwork xml:id="webwork-TaC-curvature-5">
-            <pg-code>
-            </pg-code> -->
+      <exercise label="TaC-curvature-5" language="math" component="web">
             <statement>
               <p>
                 Rearrange the blocks to form a valid identity.
@@ -1261,7 +1258,19 @@
               <block order="9" correct="no"><m>\pi</m></block>
               <block order="5" correct="no"><m>\unitnormal(t)</m></block>
             </blocks>
-        <!--</webwork>-->
+      </exercise>
+
+      <exercise label="TaC-curvature-5" component="pdf">
+        <statement>
+          <p>
+            Complete the identity: <m>\unittangentprime(s) = <fillin/>\unitnormal(s)</m>.
+          </p>
+        </statement>
+        <answer>
+          <p>
+            <m>\kappa</m>
+          </p>
+        </answer>
       </exercise>
 
       <exercise label="TaC-curvature-6">
diff --git a/ptx/sec_deriv_basic_rules.ptx b/ptx/sec_deriv_basic_rules.ptx
index 46d12a943..e1bc416a7 100644
--- a/ptx/sec_deriv_basic_rules.ptx
+++ b/ptx/sec_deriv_basic_rules.ptx
@@ -805,12 +805,12 @@
               What is the name of the rule which states that <m>\lzoo{x}{x^n} = nx^{n-1}</m>,
               where <m>n \gt 0</m> is an integer?
             </p>
-            <p>
+            <p component="web">
               <!-- <var name="$ans" width="20"/> -->
                <fillin width="25" answer="the power rule"/>
             </p>
           </statement>
-          <evaluation>
+          <evaluation component="web">
             <evaluate>
 
               <test correct="yes">
diff --git a/ptx/sec_deriv_prodquot.ptx b/ptx/sec_deriv_prodquot.ptx
index 77b2f39bb..f937997a0 100644
--- a/ptx/sec_deriv_prodquot.ptx
+++ b/ptx/sec_deriv_prodquot.ptx
@@ -913,12 +913,12 @@
             <p>
               What derivative rule is used to extend the Power Rule to include negative integer exponents?
             </p>
-            <p>
+            <p component="web">
               <!-- <var name="$ans" width="80"/> -->
               <fillin width="30" answer="the quotient rule"/>
             </p>
           </statement>
-          <evaluation>
+          <evaluation component="web">
             <evaluate>
 
               <test correct="yes">
diff --git a/ptx/sec_double_int_polar.ptx b/ptx/sec_double_int_polar.ptx
index 73a598853..c6a4dfcdf 100644
--- a/ptx/sec_double_int_polar.ptx
+++ b/ptx/sec_double_int_polar.ptx
@@ -981,9 +981,8 @@
             </pg-code> -->
             <statement>
               <p>
-                Match each element on the left to the corresponding element on the right,
+                Match the correct elements on the left to the corresponding elements on the right,
                 so that <m>\iint_R f(x,y)\, dA</m> is correctly converted to polar coordinates.
-                Not all cards will be used.
               </p>
             </statement>
             <cardsort>
diff --git a/ptx/sec_multi_chain.ptx b/ptx/sec_multi_chain.ptx
index 0be906ca1..ad854ac95 100644
--- a/ptx/sec_multi_chain.ptx
+++ b/ptx/sec_multi_chain.ptx
@@ -841,7 +841,7 @@
         <!-- </webwork> -->
       </exercise>
 
-      <exercise label="TaC-multi-chain-3" language="natural">
+      <exercise label="TaC-multi-chain-3" language="math" component="web">
         <!-- <webwork xml:id="webwork-TaC-multi-chain-3">
             <pg-code>
             </pg-code> -->
@@ -864,6 +864,23 @@
         <!-- </webwork> -->
       </exercise>
 
+      <exercise label="TaC-multi-chain-3" component="pdf">
+        <statement>
+          <p>
+            Fill in the blank: the Multivariable Chain Rule states
+          </p>
+
+          <p>
+            <m>\ds\frac{df}{dt}=\frac{\partial f}{\partial x}\cdot</m><fillin/> <m>+</m> <fillin/><m>\cdot\frac{dy}{dt}</m>.
+          </p>
+        </statement>
+        <solution>
+          <p>
+            <m>\frac{dx}{dt}</m>, and <m>\frac{\partial f}{\partial y}</m>
+          </p>
+        </solution>
+      </exercise>
+
       <exercise label="TaC-multi-chain-4">
         <!-- <webwork xml:id="webwork-TaC-multi-chain-4">
             <pg-code>
diff --git a/publication/publication-accelerated-print.ptx b/publication/publication-accelerated-print.ptx
index 5d32684d6..13e918e32 100644
--- a/publication/publication-accelerated-print.ptx
+++ b/publication/publication-accelerated-print.ptx
@@ -5,7 +5,7 @@
     <!-- Relative path, relative to "main" source file -->
     <source>
         <directories external="../assets" generated="../generated-assets-accelerated-print"/>
-        <version include="main print video taypoly-early video-early"/>
+        <version include="main print video taypoly-early video-early pdf"/>
     </source>
 
     <webwork server="https://webwork-dev.uleth.ca" course="apex-acc-print"/>
diff --git a/publication/publication-accelerated.ptx b/publication/publication-accelerated.ptx
index 4505c5891..6d6abd6c1 100644
--- a/publication/publication-accelerated.ptx
+++ b/publication/publication-accelerated.ptx
@@ -5,7 +5,7 @@
     <!-- Relative path, relative to "main" source file -->
     <source>
         <directories external="../assets" generated="../generated-assets-accelerated"/>
-        <version include="main color video taypoly-early video-early"/>
+        <version include="main color video taypoly-early video-early pdf"/>
     </source>
 
     <webwork server="https://webwork-dev.uleth.ca" course="apex-accelerated"/>
diff --git a/publication/publication-color-print-novideo.ptx b/publication/publication-color-print-novideo.ptx
index a2fec9063..2706b4b31 100644
--- a/publication/publication-color-print-novideo.ptx
+++ b/publication/publication-color-print-novideo.ptx
@@ -5,7 +5,7 @@
     <!-- Relative path, relative to "main" source file -->
     <source>
         <directories external="../assets" generated="../generated-assets"/>
-        <version include="main color novideo taypoly-late"/>
+        <version include="main color novideo taypoly-late pdf"/>
     </source>
 
     <webwork server="https://webwork-dev.uleth.ca" course="apex-main"/>
diff --git a/publication/publication-color-print.ptx b/publication/publication-color-print.ptx
index 41ba9e57f..48d49d07a 100644
--- a/publication/publication-color-print.ptx
+++ b/publication/publication-color-print.ptx
@@ -5,7 +5,7 @@
     <!-- Relative path, relative to "main" source file -->
     <source>
         <directories external="../assets" generated="../generated-assets"/>
-        <version include="main color video taypoly-late video-late"/>
+        <version include="main color video taypoly-late video-late pdf"/>
     </source>
 
     <webwork server="https://webwork-dev.uleth.ca" course="apex-main"/>
diff --git a/publication/publication-novid-print.ptx b/publication/publication-novid-print.ptx
index a3d9b3085..cafd3123d 100644
--- a/publication/publication-novid-print.ptx
+++ b/publication/publication-novid-print.ptx
@@ -5,7 +5,7 @@
     <!-- Relative path, relative to "main" source file -->
     <source>
         <directories external="../assets" generated="../generated-assets-print"/>
-        <version include="main print novideo taypoly-late"/>
+        <version include="main print novideo taypoly-late pdf"/>
     </source>
 
     <webwork server="https://webwork-dev.uleth.ca" course="apex-print"/>
diff --git a/publication/publication-print.ptx b/publication/publication-print.ptx
index 8449124a4..fc46c9c5f 100644
--- a/publication/publication-print.ptx
+++ b/publication/publication-print.ptx
@@ -5,7 +5,7 @@
     <!-- Relative path, relative to "main" source file -->
     <source>
         <directories external="../assets" generated="../generated-assets-print"/>
-        <version include="main print video taypoly-late video-late"/>
+        <version include="main print video taypoly-late video-late pdf"/>
     </source>
 
     <webwork server="https://webwork-dev.uleth.ca" course="apex-print"/>
diff --git a/publication/publication-standard-print.ptx b/publication/publication-standard-print.ptx
index 71201e6c4..28df14e07 100644
--- a/publication/publication-standard-print.ptx
+++ b/publication/publication-standard-print.ptx
@@ -5,7 +5,7 @@
     <!-- Relative path, relative to "main" source file -->
     <source>
         <directories external="../assets" generated="../generated-assets-standard-print"/>
-        <version include="main print video taypoly-early video-early"/>
+        <version include="main print video taypoly-early video-early pdf"/>
     </source>
 
     <webwork server="https://webwork-dev.uleth.ca" course="apex-std-print"/>
diff --git a/publication/publication-standard.ptx b/publication/publication-standard.ptx
index e10478522..ea2b6a5bb 100644
--- a/publication/publication-standard.ptx
+++ b/publication/publication-standard.ptx
@@ -5,7 +5,7 @@
     <!-- Relative path, relative to "main" source file -->
     <source>
         <directories external="../assets" generated="../generated-assets-standard"/>
-        <version include="main color video taypoly-early video-early"/>
+        <version include="main color video taypoly-early video-early pdf"/>
     </source>
 
     <webwork server="https://webwork-dev.uleth.ca" course="apex-standard"/>

From a6897becc637a880c48039686ab6852b99920052 Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Tue, 2 Jun 2026 16:39:24 -0600
Subject: [PATCH 05/18] remove grid background from graph

---
 ptx/sec_deriv_inverse_function.ptx | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/ptx/sec_deriv_inverse_function.ptx b/ptx/sec_deriv_inverse_function.ptx
index 415ed6110..7a5793bbc 100644
--- a/ptx/sec_deriv_inverse_function.ptx
+++ b/ptx/sec_deriv_inverse_function.ptx
@@ -151,7 +151,7 @@
       ymin=-1.3,ymax=2,
       xmin=-1.3,xmax=2,
       clip=false,
-      grid=both,
+      %grid=both,
       xtick={-1,1},
       ytick={-1,1},
       minor xtick={-1.25,-1,...,2},
@@ -736,7 +736,7 @@
 
   <pagebreak-latex/>
   
-  <theorem xml:id="thm_deriv_glossary" hstretch="420">
+  <theorem xml:id="thm_deriv_glossary" hstretch="420" hskip="120">
     <title>Glossary of Derivatives of Elementary Functions</title>
     <statement>
       <p>
@@ -1432,11 +1432,13 @@
         </exercise>
       </exercisegroup>
 
+      <enlarge-page skipsize="2"/>
+      
       <exercisegroup cols="2" xml:id="exset-deriv-inverse-two-ways">
         <introduction>
           <p>
             Compute the derivative of the given function in two ways:
-            <ol>
+            <ol cols="2">
               <li>
                 <p>
                   By simplifying first, then taking the derivative, and

From a65365c7fbb384414ee75601cba428612eb59cac Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Tue, 2 Jun 2026 16:40:10 -0600
Subject: [PATCH 06/18] add components to stray proteus exercises

---
 ptx/sec_improper_integration.ptx |  2 +-
 ptx/sec_param_eqs.ptx            |  4 ++--
 ptx/sec_ratio_root_tests.ptx     |  2 +-
 ptx/sec_substitution.ptx         | 10 +++++-----
 publication/publication.ptx      |  2 +-
 5 files changed, 10 insertions(+), 10 deletions(-)

diff --git a/ptx/sec_improper_integration.ptx b/ptx/sec_improper_integration.ptx
index 28a358887..d3bb81624 100644
--- a/ptx/sec_improper_integration.ptx
+++ b/ptx/sec_improper_integration.ptx
@@ -1209,7 +1209,7 @@
       </solution>
     </example>
 
-    <exercise label="APEX-PROTEUS-improper-int-2-v1">
+    <exercise label="APEX-PROTEUS-improper-int-2-v1" component="proteus">
       <title>PROTEUS EXERCISE</title>
       <statement>
         <p>
diff --git a/ptx/sec_param_eqs.ptx b/ptx/sec_param_eqs.ptx
index f2b23e18a..bd91e4c0a 100644
--- a/ptx/sec_param_eqs.ptx
+++ b/ptx/sec_param_eqs.ptx
@@ -733,7 +733,7 @@
       </solution>
     </example>
 
-    <exercise label="APEX-PROTEUS-param-eqs-5-v1">
+    <exercise label="APEX-PROTEUS-param-eqs-5-v1" component="proteus">
       <title>PROTEUS EXERCISE</title>
       <statement>
         <p>
@@ -1224,7 +1224,7 @@
       </solution>
     </exercise>
 
-    <exercise label="APEX-PROTEUS-param-eqs-4-v1">
+    <exercise label="APEX-PROTEUS-param-eqs-4-v1" component="proteus">
       <title>PROTEUS EXERCISE</title>
       <statement>
         <p>
diff --git a/ptx/sec_ratio_root_tests.ptx b/ptx/sec_ratio_root_tests.ptx
index e80087f7e..1ae8f6673 100644
--- a/ptx/sec_ratio_root_tests.ptx
+++ b/ptx/sec_ratio_root_tests.ptx
@@ -430,7 +430,7 @@
       </cardsort> 
     </exercise>
 
-    <exercise label="APEX-PROTEUS-ratio-root-3-v1">
+    <exercise label="APEX-PROTEUS-ratio-root-3-v1" component="proteus">
       <title>PROTEUS EXERCISE</title>
       <statement>
         <p>
diff --git a/ptx/sec_substitution.ptx b/ptx/sec_substitution.ptx
index c6bc37f0c..4814a53e8 100644
--- a/ptx/sec_substitution.ptx
+++ b/ptx/sec_substitution.ptx
@@ -150,7 +150,7 @@
       </statement>
     </theorem>
 
-    <exercise label="APEX-PROTEUS-substitution-1-v1">
+    <exercise label="APEX-PROTEUS-substitution-1-v1" component="proteus">
       <title>PROTEUS EXERCISE</title>
       <statement>
         <p>
@@ -314,7 +314,7 @@
       <video youtube="-6CFSvtMCDU" label="vid_int_sub_examples_1"/>
     </figure>
 
-    <exercise label="APEX-PROTEUS-substitution-2-v1">
+    <exercise label="APEX-PROTEUS-substitution-2-v1" component="proteus">
       <title>PROTEUS EXERCISE</title>
       
       <statement>
@@ -1149,7 +1149,7 @@
       </statement>
     </theorem>
 
-    <exercise label="APEX-PROTEUS-substitution-3-v1">
+    <exercise label="APEX-PROTEUS-substitution-3-v1" component="proteus">
       <title>PROTEUS EXERCISE</title>
       <statement>
         <p>
@@ -1483,12 +1483,12 @@
             <p>
               Substitution <q>undoes</q> what derivative rule?
             </p>
-            <p>
+            <p componet="web">
               <!-- <var name="'the Chain Rule'" width="40"/> -->
                <fillin width="30" answer="the chain rule"/>
             </p>
           </statement>
-          <evaluation>
+          <evaluation component="web">
             <evaluate>
 
               <test correct="yes">
diff --git a/publication/publication.ptx b/publication/publication.ptx
index 6220c3ee6..f6ab24cf8 100644
--- a/publication/publication.ptx
+++ b/publication/publication.ptx
@@ -5,7 +5,7 @@
     <!-- Relative path, relative to "main" source file -->
     <source>
         <directories external="../assets" generated="../generated-assets"/>
-        <version include="main color video taypoly-late video-late"/>
+        <version include="main color video taypoly-late video-late pdf"/>
     </source>
 
     <webwork server="https://webwork-dev.uleth.ca" course="apex-main"/>

From b162ebc1ffc9fd4b1ba1375902171fcac4042c21 Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Tue, 2 Jun 2026 16:40:33 -0600
Subject: [PATCH 07/18] add space above insight tcolorbox

---
 xsl/apex-latex-print-color.xsl | 2 +-
 xsl/apex-latex-print-style.xsl | 2 +-
 xsl/apex-latex-style.xsl       | 2 +-
 3 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/xsl/apex-latex-print-color.xsl b/xsl/apex-latex-print-color.xsl
index f834a7150..83786fdfb 100644
--- a/xsl/apex-latex-print-color.xsl
+++ b/xsl/apex-latex-print-color.xsl
@@ -59,7 +59,7 @@
 </xsl:template>
 
 <xsl:template match="insight" mode="tcb-style">
-    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, colbacktitle=red!60!black!20, colframe=red!30!black!50, colback=white!95!red, coltitle=black, titlerule=-0.3pt,</xsl:text>
+    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, before skip = \baselineskip, colbacktitle=red!60!black!20, colframe=red!30!black!50, colback=white!95!red, coltitle=black, titlerule=-0.3pt,</xsl:text>
 </xsl:template>
 
 <xsl:template match="&DEFINITION-LIKE;" mode="tcb-style">
diff --git a/xsl/apex-latex-print-style.xsl b/xsl/apex-latex-print-style.xsl
index 588249e89..98d595976 100644
--- a/xsl/apex-latex-print-style.xsl
+++ b/xsl/apex-latex-print-style.xsl
@@ -59,7 +59,7 @@
 </xsl:template>
 
 <xsl:template match="insight" mode="tcb-style">
-    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, colbacktitle=white, colframe=black, colback=white, coltitle=black, titlerule=-0.3pt,</xsl:text>
+    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, before skip = \baselineskip, colbacktitle=white, colframe=black, colback=white, coltitle=black, titlerule=-0.3pt,</xsl:text>
 </xsl:template>
 
 <xsl:template match="&DEFINITION-LIKE;" mode="tcb-style">
diff --git a/xsl/apex-latex-style.xsl b/xsl/apex-latex-style.xsl
index 2c4c53702..4acd21f80 100644
--- a/xsl/apex-latex-style.xsl
+++ b/xsl/apex-latex-style.xsl
@@ -59,7 +59,7 @@
 </xsl:template>
 
 <xsl:template match="insight" mode="tcb-style">
-    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, colbacktitle=red!60!black!20, colframe=red!30!black!50, colback=white!95!red, coltitle=black, titlerule=-0.3pt,</xsl:text>
+    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, before skip = \baselineskip, colbacktitle=red!60!black!20, colframe=red!30!black!50, colback=white!95!red, coltitle=black, titlerule=-0.3pt,</xsl:text>
 </xsl:template>
 
 <xsl:template match="&DEFINITION-LIKE;" mode="tcb-style">

From a3acb6b7919265571bd579e75f5e685fc81d3b9a Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Tue, 2 Jun 2026 16:40:58 -0600
Subject: [PATCH 08/18] adjust display equations

---
 ptx/sec_deriv_chainrule.ptx | 13 ++++++++++---
 ptx/sec_differentials.ptx   |  6 +-----
 2 files changed, 11 insertions(+), 8 deletions(-)

diff --git a/ptx/sec_deriv_chainrule.ptx b/ptx/sec_deriv_chainrule.ptx
index 43ba6dd30..2bddf0241 100644
--- a/ptx/sec_deriv_chainrule.ptx
+++ b/ptx/sec_deriv_chainrule.ptx
@@ -899,7 +899,7 @@
     <title>Using the Product, Quotient and Chain Rules</title>
     <statement>
       <p>
-        Find the derivative of <m>f(x) = \frac{x\cos(x^{-2})-\sin^2(e^{4x})}{\ln(x^2+5x^4)}</m>.
+        Find the derivative of <m>f(x) = \dfrac{x\cos(x^{-2})-\sin^2(e^{4x})}{\ln(x^2+5x^4)}</m>.
       </p>
     </statement>
     <solution>
@@ -909,13 +909,18 @@
         It employs the <xref ref="thm_QuotientRule" text="title"/>,
         the <xref ref="thm_ProductRule" text="title"/>,
         and the <xref ref="thm_chain_rule" text="title"/> three times.
-        <md>
+        <!-- <md>
           <mrow>\amp\fp(x)</mrow>
           <mrow>\amp=\Bigg(\ln\mathopen{}\left(x^2+5x^4\right)\mathclose{}\cdot\bigg[\Big(x\cdot\left(-\sin\mathopen{}\left(x^{-2}\right)\mathclose{}\right)\cdot\left(-2x^{-3}\right)</mrow>
           <mrow>\amp\qquad{}+1\cdot \cos\mathopen{}\left(x^{-2}\right)\Big)-2\sin\mathopen{}\left(e^{4x}\right)\mathclose{}\cdot\cos\mathopen{}\left(e^{4x}\right)\mathclose{}\cdot\left(4e^{4x}\right)\bigg]</mrow>
           <mrow>\amp\qquad\qquad\qquad{}-\left(x\cos\mathopen{}\left(x^{-2}\right)\mathclose{}-\sin^2\mathopen{}\left(e^{4x}\right)\mathclose{}\right)\cdot\frac{2x+20x^3}{x^2+5x^4}\Bigg)</mrow>
           <mrow>\amp\phantom{{}={}}\left/\left(\ln\mathopen{}\left(x^2+5x^4\right)\mathclose{}\right)^2\right.</mrow>
-        </md>.
+        </md>. -->
+        <md>
+          f'(x)=\frac{\begin{matrix}\ln\left(x^2+5x^4\right)\cdot\bigg[\Big(x\cdot\left(-\sin\left(x^{-2}\right)\right)\cdot\left(-2x^{-3}\right)+1\cdot \cos\left(x^{-2}\right)\Big)\hspace{60pt}\\
+          \hspace{72pt}-2\sin\left(e^{4x}\right)\cdot\cos\left(e^{4x}\right)\cdot\left(4e^{4x}\right)\bigg]\\
+          \hspace{120pt}-\left(x\cos\left(x^{-2}\right)-\sin^2\left(e^{4x}\right)\right)\cdot\frac{2x+20x^3}{x^2+5x^4}\end{matrix}}{\left(\ln\left(x^2+5x^4\right)\right)^2}
+        </md>.        
       </p>
 
       <p>
@@ -2125,6 +2130,8 @@
         </exercise>
       </exercisegroup>
 
+      <enlarge-page skipsize="2"/>
+
       <exercise label="ex-deriv-chain-tangent-5">
         <webwork xml:id="webwork-ex-deriv-chain-tangent-5">
           <pg-code>
diff --git a/ptx/sec_differentials.ptx b/ptx/sec_differentials.ptx
index 3de6f1b7e..e16fc05f3 100644
--- a/ptx/sec_differentials.ptx
+++ b/ptx/sec_differentials.ptx
@@ -549,11 +549,7 @@
         We approximate the difference between <m>f(4.5)</m> and <m>f(4)</m> using differentials,
         with <m>dx = 0.5</m>:
         <md>
-          <mrow>f(4.5)-f(4) \amp = \dy \approx dy</mrow>
-          <mrow>\amp = \fp(4)\cdot dx</mrow>
-          <mrow>\amp = 1/4 \cdot 1/2</mrow>
-          <mrow>\amp = 1/8</mrow>
-          <mrow>\amp = 0.125</mrow>
+          f(4.5)-f(4) = \dy \approx dy = \fp(4)\cdot dx = \frac14 \cdot \frac12 = \frac18 = 0.125
         </md>.
       </p>
 

From d2a308ae31baa746332dd03e98880023bce4018d Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Tue, 2 Jun 2026 16:41:13 -0600
Subject: [PATCH 09/18] replace tables with md

---
 ptx/sec_taylor_poly.ptx   | 140 +++++++++++++++++++++++++++++++-------
 ptx/sec_taylor_series.ptx |  47 ++++++++++---
 2 files changed, 153 insertions(+), 34 deletions(-)

diff --git a/ptx/sec_taylor_poly.ptx b/ptx/sec_taylor_poly.ptx
index f9da0f229..278bfd030 100644
--- a/ptx/sec_taylor_poly.ptx
+++ b/ptx/sec_taylor_poly.ptx
@@ -75,7 +75,16 @@
       <!-- figures/fig_taypolyintroa.tex END -->
       <figure xml:id="fig_taypolyintroa_2">
         <caption>Derivatives of <m>f</m> evaluated at <m>0</m></caption>
-        <tabular>
+        <sidebyside>
+          <p>
+            <md>
+              <mrow>f(0) \amp = 2 \amp \fp''(0) \amp =-1</mrow>
+              <mrow>\fp(0) \amp = 1 \amp f^{(4)}(0) \amp = -12</mrow>
+              <mrow>\fpp(0) \amp = 2 \amp f^{(5)}(0) \amp = -19</mrow>
+            </md>
+          </p>
+        </sidebyside>
+        <!-- <tabular>
           <row>
             <cell><m>f(0) = 2</m></cell>
             <cell/>
@@ -91,7 +100,7 @@
             <cell/>
             <cell><m>f^{(5)}(0)=-19</m></cell>
           </row>
-        </tabular>
+        </tabular> -->
       </figure>
     </sidebyside>
 
@@ -214,7 +223,7 @@
       whose first four derivatives at 0 match those of <m>f</m>.
     </p>
 
-    <figure xml:id="fig_taypolyintrob" vshift="0">
+    <figure xml:id="fig_taypolyintrob" vshift="1">
       <caption>Plotting <m>f</m>, <m>p_2</m> and <m>p_4</m></caption>
       <!-- START figures/fig_taypolyintrob.tex -->
       <image width="47%">
@@ -351,7 +360,7 @@
       </md>.
     </p>
 
-    <figure xml:id="fig_taypolyintroc" vshift="-2">
+    <figure xml:id="fig_taypolyintroc" vshift="-1">
       <caption>Plotting <m>f</m> and <m>p_{13}</m></caption>
       <!-- START figures/fig_taypolyintroc.tex -->
       <image width="47%">
@@ -533,7 +542,18 @@
 
               <figure xml:id="fig_taypoly1a" vshift="-2">
                 <caption>The derivatives of <m>f(x)=e^x</m> evaluated at <m>x=0</m></caption>
-                <tabular>
+                <sidebyside>
+                  <p>
+                    <md>
+                      <mrow>f(x) \amp = e^x \amp f(0) \amp = 1</mrow>
+                      <mrow>\fp(x) \amp = e^x \amp \fp(0) \amp =1</mrow>
+                      <mrow>\fp'(x) \amp = e^x \amp \fp'(0) \amp =1</mrow>
+                      <mrow> \amp \vdots \amp \amp \vdots</mrow>
+                      <mrow>f^{(n)}(x) \amp = e^x \amp f^{(n)}(0) \amp =1</mrow>
+                    </md>
+                  </p>
+                </sidebyside>
+                <!-- <tabular>
                   <row>
                     <cell><m>f(x) = e^x</m></cell>
                     <cell><m>f(0) = 1</m></cell>
@@ -554,7 +574,7 @@
                     <cell><m>f\,^{(n)}(x) = e^x</m></cell>
                     <cell><m>f\,^{(n)}(0) = 1</m></cell>
                   </row>
-                </tabular>
+                </tabular> -->
               </figure>
 
               <p>
@@ -720,7 +740,21 @@
 
               <figure xml:id="fig_taypoly2a" vshift="-7">
                 <caption>Derivatives of <m>\ln(x)</m> evaluated at <m>x=1</m></caption>
-                <tabular>
+                <sidebyside>
+                  <p>
+                    <md>
+                      <mrow>f(x) \amp = \ln(x) \amp f(1) \amp = 0</mrow>
+                      <mrow>\fp(x) \amp = \frac1x \amp \fp(1) \amp = 1</mrow>
+                      <mrow>\fp'(x) \amp = -\frac{1}{x^2} \amp \fp'(1) \amp = -1 </mrow>
+                      <mrow>\fp''(x) \amp = \frac{2}{x^3} \amp \fp''(1) \amp = 2</mrow>
+                      <mrow>f^{(4)}(x) \amp = -\frac{6}{x^4} \amp f^{(4)}(1) \amp = -6</mrow>
+                      <mrow> \amp \vdots \amp \amp \vdots</mrow>
+                      <mrow>f^{(n)}(x) \amp = \amp f^{(n)}(1) \amp =</mrow>
+                      <mrow>\frac{(-1)^{n+1}(n-1)!}{x^n} \amp \amp (-1)^{n+1}(n-1)! </mrow>
+                    </md>
+                  </p>
+                </sidebyside>
+                <!-- <tabular>
                   <row>
                     <cell><m>f(x) = \ln(x)</m></cell>
                     <cell><m>f(1) = 0</m></cell>
@@ -753,7 +787,7 @@
                     <cell><m>\frac{(-1)^{n+1}(n-1)!}{x^n}</m></cell>
                     <cell><m>\!\!(-1)^{n+1}(n-1)!</m></cell>
                   </row>
-                </tabular>
+                </tabular> -->
               </figure>
 
               <p>
@@ -1205,7 +1239,23 @@
 
         <figure xml:id="fig_taypoly4a" vshift="4" component="taypoly-late">
           <caption>A table of the derivatives of <m>f(x)=\cos(x)</m> evaluated at <m>x=0</m></caption>
-          <tabular>
+          <sidebyside>
+            <p>
+              <md>
+                <mrow>f(x) \amp = \cos(x) \amp f(0) \amp = 1</mrow>
+                <mrow>f'(x) \amp = -\sin(x) \amp \fp(0) \amp = 0</mrow>
+                <mrow>\fp'(x) \amp = -\cos(x) \amp \fp'(0) \amp = -1</mrow>
+                <mrow>\fp''(x) \amp = \sin(x) \amp \fp''(0) \amp = 0</mrow>
+                <mrow>f^{(4)}(x) \amp = \cos(x) \amp f^{(4)}(0) \amp =1</mrow>
+                <mrow>f^{(5)}(x) \amp = -\sin(x) \amp f^{(5)}(0) \amp =0</mrow>
+                <mrow>f^{(6)}(x) \amp = -\cos(x) \amp f^{(6)}(0) \amp =-1</mrow>
+                <mrow>f^{(7)}(x) \amp = \sin(x) \amp f^{(7)}(0) \amp =0</mrow>
+                <mrow>f^{(8)}(x) \amp = \cos(x) \amp f^{(8)}(0) \amp =1</mrow>
+                <mrow>f^{(9)}(x) \amp = -\sin(x) \amp f^{(9)}(0) \amp =0</mrow>
+              </md>
+            </p>
+          </sidebyside>
+          <!-- <tabular>
             <row>
               <cell><m>f(x) = \cos(x)</m></cell>
               <cell><m>f(0) = 1</m></cell>
@@ -1246,12 +1296,28 @@
               <cell><m>f^{(9)}(x) = -\sin(x)</m></cell>
               <cell><m>f^{(9)}(0) = 0</m></cell>
             </row>
-          </tabular>
+          </tabular> -->
         </figure>
 
         <figure xml:id="fig_taypoly4a-early" vshift="0" component="taypoly-early">
           <caption>A table of the derivatives of <m>f(x)=\cos(x)</m> evaluated at <m>x=0</m></caption>
-          <tabular>
+          <sidebyside>
+            <p>
+              <md>
+                <mrow>f(x) \amp = \cos(x) \amp f(0) \amp = 1</mrow>
+                <mrow>f'(x) \amp = -\sin(x) \amp \fp(0) \amp = 0</mrow>
+                <mrow>\fp'(x) \amp = -\cos(x) \amp \fp'(0) \amp = -1</mrow>
+                <mrow>\fp''(x) \amp = \sin(x) \amp \fp''(0) \amp = 0</mrow>
+                <mrow>f^{(4)}(x) \amp = \cos(x) \amp f^{(4)}(0) \amp =1</mrow>
+                <mrow>f^{(5)}(x) \amp = -\sin(x) \amp f^{(5)}(0) \amp =0</mrow>
+                <mrow>f^{(6)}(x) \amp = -\cos(x) \amp f^{(6)}(0) \amp =-1</mrow>
+                <mrow>f^{(7)}(x) \amp = \sin(x) \amp f^{(7)}(0) \amp =0</mrow>
+                <mrow>f^{(8)}(x) \amp = \cos(x) \amp f^{(8)}(0) \amp =1</mrow>
+                <mrow>f^{(9)}(x) \amp = -\sin(x) \amp f^{(9)}(0) \amp =0</mrow>
+              </md>
+            </p>
+          </sidebyside>
+          <!-- <tabular>
             <row>
               <cell><m>f(x) = \cos(x)</m></cell>
               <cell><m>f(0) = 1</m></cell>
@@ -1292,7 +1358,7 @@
               <cell><m>f^{(9)}(x) = -\sin(x)</m></cell>
               <cell><m>f^{(9)}(0) = 0</m></cell>
             </row>
-          </tabular>
+          </tabular> -->
         </figure>
 
         <p>
@@ -1332,7 +1398,7 @@
           Note how well the two functions agree on about <m>(-\pi,\pi)</m>.
         </p>
 
-        <figure xml:id="fig_taypoly4b" vshift="1" component="taypoly-late">
+        <figure xml:id="fig_taypoly4b" vshift="3" component="taypoly-late">
           <caption>A graph of <m>f(x)= \cos(x)</m> and its degree 8 Maclaurin
           polynomial</caption>
           <!-- START figures/fig_taypoly4.tex -->
@@ -1510,22 +1576,33 @@
                 This is done in <xref ref="fig_taypoly5a" component="taypoly-late"/><xref ref="fig_taypoly5a-early" component="taypoly-early"/>.
               </p>
 
-              <figure xml:id="fig_taypoly5a" vshift="0" component="taypoly-late">
+              <figure xml:id="fig_taypoly5a" vshift="2" component="taypoly-late">
                 <caption>A table of the derivatives of <m>f(x)=\sqrt{x}</m> evaluated at <m>x=4</m></caption>
-                <tabular>
-                  <row>
+                <sidebyside>
+                  <p>
+                    <md>
+                      <mrow>f(x) \amp = \sqrt{x} \amp f(4) \amp = 2</mrow>
+                      <mrow>\fp(x) \amp = \frac{1}{2\sqrt{x}} \amp \fp(4) \amp = \frac14</mrow>
+                      <mrow>\fp'(x) \amp = \frac{-1}{4x^{3/2}} \amp \fp'(4) \amp = \frac{-1}{32}</mrow>
+                      <mrow>\fp''(x) \amp = \frac{3}{8x^{5/2}} \amp \fp''(4) \amp = \frac{3}{256}</mrow>
+                      <mrow>f^{(4)}(x) \amp = \frac{-15}{16x^{7/2}} \amp f^{(4)}(4) \amp = \frac{-15}{2048}</mrow>
+                    </md>
+                  </p>
+                </sidebyside>
+                <!-- <tabular>
+                  <row height="10pt">
                     <cell><m>f(x) = \sqrt{x}</m></cell>
                     <cell><m>f(4) = 2</m></cell>
                   </row>
-                  <row>
-                    <cell><m>\ds\fp(x) = \frac{1}{2\sqrt{x}}</m></cell>
-                    <cell><m>\ds\fp(4) = \frac{1}{4}</m></cell>
+                  <row height="10pt">
+                    <cell><m>\ds \fp(x) = \frac{1}{2\sqrt{x}}</m></cell>
+                    <cell><m>\ds \fp(4) = \frac{1}{4}</m></cell>
                   </row>
-                  <row>
-                    <cell><m>\ds\fp'(x) = \frac{-1}{4x^{3/2}}</m></cell>
-                    <cell><m>\ds\fp'(4) = \frac{-1}{32}</m></cell>
+                  <row height="10pt">
+                    <cell><m>\ds \fp'(x) = \frac{-1}{4x^{3/2}}</m></cell>
+                    <cell><m>\ds \fp'(4) = \frac{-1}{32}</m></cell>
                   </row>
-                  <row>
+                  <row height="10pt">
                     <cell><m>\ds\fp''(x) = \frac3{8x^{5/2}}</m></cell>
                     <cell><m>\ds\fp''(4) = \frac{3}{256}</m></cell>
                   </row>
@@ -1533,12 +1610,23 @@
                     <cell><m>\ds f^{(4)}(x) = \frac{-15}{16x^{7/2}}</m></cell>
                     <cell><m>\ds f^{(4)}(4) = \frac{-15}{2048}</m></cell>
                   </row>
-                </tabular>
+                </tabular> -->
               </figure>
 
               <figure xml:id="fig_taypoly5a-early" vshift="-4.5" component="taypoly-early">
                 <caption>A table of the derivatives of <m>f(x)=\sqrt{x}</m> evaluated at <m>x=4</m></caption>
-                <tabular>
+                <sidebyside>
+                  <p>
+                    <md>
+                      <mrow>f(x) \amp = \sqrt{x} \amp f(4) \amp = 2</mrow>
+                      <mrow>\fp(x) \amp = \frac{1}{2\sqrt{x}} \amp \fp(4) \amp = \frac14</mrow>
+                      <mrow>\fp'(x) \amp = \frac{-1}{4x^{3/2}} \amp \fp'(4) \amp = \frac{-1}{32}</mrow>
+                      <mrow>\fp''(x) \amp = \frac{3}{8x^{5/2}} \amp \fp''(4) \amp = \frac{3}{256}</mrow>
+                      <mrow>f^{(4)}(x) \amp = \frac{-15}{16x^{7/2}} \amp f^{(4)}(4) \amp = \frac{-15}{2048}</mrow>
+                    </md>
+                  </p>
+                </sidebyside>
+                <!-- <tabular>
                   <row>
                     <cell><m>f(x) = \sqrt{x}</m></cell>
                     <cell><m>f(4) = 2</m></cell>
@@ -1559,7 +1647,7 @@
                     <cell><m>\ds f^{(4)}(x) = \frac{-15}{16x^{7/2}}</m></cell>
                     <cell><m>\ds f^{(4)}(4) = \frac{-15}{2048}</m></cell>
                   </row>
-                </tabular>
+                </tabular> -->
               </figure>
 
               <p>
diff --git a/ptx/sec_taylor_series.ptx b/ptx/sec_taylor_series.ptx
index 266453914..bc1a14259 100644
--- a/ptx/sec_taylor_series.ptx
+++ b/ptx/sec_taylor_series.ptx
@@ -95,7 +95,23 @@
 
       <figure xml:id="fig_ts1" vshift="-3">
         <caption>Derivatives of <m>f(x)=\cos (x)</m> evaluated at <m>x=0</m></caption>
-        <tabular>
+        <sidebyside>
+          <p>
+            <md>
+              <mrow>f(x) \amp = \cos(x) \amp f(0) \amp = 1</mrow>
+              <mrow>f'(x) \amp = -\sin(x) \amp \fp(0) \amp = 0</mrow>
+              <mrow>\fp'(x) \amp = -\cos(x) \amp \fp'(0) \amp = -1</mrow>
+              <mrow>\fp''(x) \amp = \sin(x) \amp \fp''(0) \amp = 0</mrow>
+              <mrow>f^{(4)}(x) \amp = \cos(x) \amp f^{(4)}(0) \amp =1</mrow>
+              <mrow>f^{(5)}(x) \amp = -\sin(x) \amp f^{(5)}(0) \amp =0</mrow>
+              <mrow>f^{(6)}(x) \amp = -\cos(x) \amp f^{(6)}(0) \amp =-1</mrow>
+              <mrow>f^{(7)}(x) \amp = \sin(x) \amp f^{(7)}(0) \amp =0</mrow>
+              <mrow>f^{(8)}(x) \amp = \cos(x) \amp f^{(8)}(0) \amp =1</mrow>
+              <mrow>f^{(9)}(x) \amp = -\sin(x) \amp f^{(9)}(0) \amp =0</mrow>
+            </md>
+          </p>
+        </sidebyside>
+        <!-- <tabular>
           <row>
             <cell><m>f(x) = \cos(x)</m></cell>
             <cell><m>f(0) = 1</m></cell>
@@ -136,7 +152,7 @@
             <cell><m>f^{(9)}(x) = -\sin(x)</m></cell>
             <cell><m>f^{(9)}(0) = 0</m></cell>
           </row>
-        </tabular>
+        </tabular> -->
       </figure>
 
       <p>
@@ -217,7 +233,22 @@
 
       <figure xml:id="fig_ts2" vshift="-4">
         <caption>Derivatives of <m>\ln(x)</m> evaluated at <m>x=1</m></caption>
-        <tabular>
+        <sidebyside>
+          <p>
+            <md>
+              <mrow>f(x) \amp = \ln(x) \amp f(1) \amp = 0</mrow>
+              <mrow>\fp(x) \amp = \frac1x \amp \fp(1) \amp = 1</mrow>
+              <mrow>\fp'(x) \amp = -\frac{1}{x^2} \amp \fp'(1) \amp = -1 </mrow>
+              <mrow>\fp''(x) \amp = \frac{2}{x^3} \amp \fp''(1) \amp = 2</mrow>
+              <mrow>f^{(4)}(x) \amp = -\frac{6}{x^4} \amp f^{(4)}(1) \amp = -6</mrow>
+              <mrow>f^{(5)}(x) \amp = \frac{24}{x^5} \amp f^{(5)}(1) \amp = 24</mrow>
+              <mrow> \amp \vdots \amp \amp \vdots</mrow>
+              <mrow>f^{(n)}(x) \amp = \amp f^{(n)}(1) \amp =</mrow>
+              <mrow>\frac{(-1)^{n+1}(n-1)!}{x^n} \amp \amp (-1)^{n+1}(n-1)! </mrow>
+            </md>
+          </p>
+        </sidebyside>
+        <!-- <tabular>
           <row>
             <cell><m>f(x) = \ln(x)</m></cell>
             <cell><m>f(1) = 0</m></cell>
@@ -243,8 +274,8 @@
             <cell><m>f^{(5)}(1) = 24</m></cell>
           </row>
           <row>
-            <cell><m>\, \vdots</m></cell>
-            <cell><m>\, \vdots</m></cell>
+            <cell halign="center"><m>\vdots</m></cell>
+            <cell halign="center"><m>\vdots</m></cell>
           </row>
           <row>
             <cell><m>f^{(n)}(x) =</m></cell>
@@ -254,7 +285,7 @@
             <cell><m>\ds \frac{(-1)^{n+1}(n-1)!}{x^n}</m></cell>
             <cell><m>(-1)^{n+1}(n-1)!</m></cell>
           </row>
-        </tabular>
+        </tabular> -->
       </figure>
 
       <p>
@@ -696,12 +727,12 @@
     </p>
   </insight>
 
-  <aside vshift="-1">
+  <aside vshift="-4">
     <p>
       Note that we require <m>h(x)</m> to be a polynomial function in <xref ref="thm_series_alg"/>.
       If we plug a function that is not polynomial into a power series,
       the result will no longer be a power series.
-      If one is <em>very</em> careful about the centre and radius of convergence,
+      If one is <em>very</em> careful about the center and radius of convergence,
       it is technically possible to substitute the Taylor series for a general function <m>h(x)</m>
       into the Taylor series for <m>f(x)</m>, and the result will be the Taylor series for <m>f(h(x))</m>.
     </p>

From 466d9aaea53d378eaadc4347887f26ec971eba26 Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Tue, 2 Jun 2026 19:32:10 -0600
Subject: [PATCH 10/18] fix array alignment

---
 ptx/sec_taylor_poly.ptx | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ptx/sec_taylor_poly.ptx b/ptx/sec_taylor_poly.ptx
index 278bfd030..fb8185770 100644
--- a/ptx/sec_taylor_poly.ptx
+++ b/ptx/sec_taylor_poly.ptx
@@ -750,7 +750,7 @@
                       <mrow>f^{(4)}(x) \amp = -\frac{6}{x^4} \amp f^{(4)}(1) \amp = -6</mrow>
                       <mrow> \amp \vdots \amp \amp \vdots</mrow>
                       <mrow>f^{(n)}(x) \amp = \amp f^{(n)}(1) \amp =</mrow>
-                      <mrow>\frac{(-1)^{n+1}(n-1)!}{x^n} \amp \amp (-1)^{n+1}(n-1)! </mrow>
+                      <mrow>(-1)^{n+1}\amp\frac{(n-1)!}{x^n} \amp (-1)^{n+1}\amp(n-1)!</mrow>
                     </md>
                   </p>
                 </sidebyside>

From 555e4f7c5e9b21fcd1863797807918e72f06df0b Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Tue, 2 Jun 2026 19:33:58 -0600
Subject: [PATCH 11/18] figure adjustment

---
 ptx/sec_multi_limit.ptx | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ptx/sec_multi_limit.ptx b/ptx/sec_multi_limit.ptx
index 69ca44907..686683a91 100644
--- a/ptx/sec_multi_limit.ptx
+++ b/ptx/sec_multi_limit.ptx
@@ -393,7 +393,7 @@
       then <m>f(x,y)</m> should be within <m>\varepsilon</m> of <m>L</m>.
     </p>
 
-    <figure xml:id="fig_multilimitdef" vshift="2">
+    <figure xml:id="fig_multilimitdef" vshift="2.5">
       <caption><em>Illustrating the definition of a limit.</em> The open disk in the <m>xy</m>-plane has radius <m>\delta</m>. Let <m>(x,y)</m> be any point in this disk; <m>f(x,y)</m> is within <m>\varepsilon</m> of <m>L</m>.</caption>
 
       <!-- START figures/figmultilimit_def_3D.asy -->

From 149896880be1438dbf96d619aa553f21386f3582 Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Tue, 2 Jun 2026 19:38:57 -0600
Subject: [PATCH 12/18] two more adjustments

---
 ptx/sec_deriv_intro.ptx   | 2 +-
 ptx/sec_taylor_series.ptx | 4 ++--
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/ptx/sec_deriv_intro.ptx b/ptx/sec_deriv_intro.ptx
index 94e5dcad8..263795376 100644
--- a/ptx/sec_deriv_intro.ptx
+++ b/ptx/sec_deriv_intro.ptx
@@ -1670,7 +1670,7 @@
           again, this limit is easier to evluate than the limit of the difference quotient.
         </p>
 
-        <figure xml:id="fig_diff_closed1" vshift="0">
+        <figure xml:id="fig_diff_closed1" vshift="2">
           <caption>A graph of <m>y=x^{1/2}</m> and <m>y=x^{3/2}</m> in <xref ref="ex_diff_closed1"/></caption>
           <image width="47%">
             <shortdescription>
diff --git a/ptx/sec_taylor_series.ptx b/ptx/sec_taylor_series.ptx
index bc1a14259..1f33d6812 100644
--- a/ptx/sec_taylor_series.ptx
+++ b/ptx/sec_taylor_series.ptx
@@ -244,7 +244,7 @@
               <mrow>f^{(5)}(x) \amp = \frac{24}{x^5} \amp f^{(5)}(1) \amp = 24</mrow>
               <mrow> \amp \vdots \amp \amp \vdots</mrow>
               <mrow>f^{(n)}(x) \amp = \amp f^{(n)}(1) \amp =</mrow>
-              <mrow>\frac{(-1)^{n+1}(n-1)!}{x^n} \amp \amp (-1)^{n+1}(n-1)! </mrow>
+              <mrow>(-1)^{n+1}\amp\frac{(n-1)!}{x^n} \amp  (-1)^{n+1}\amp (n-1)! </mrow>
             </md>
           </p>
         </sidebyside>
@@ -611,7 +611,7 @@
     which is not particularly good.
   </p>
 
-  <insight xml:id="idea_common_taylor" hstretch="375" component="taypoly-late">
+  <insight xml:id="idea_common_taylor" hstretch="375" hskip="87" component="taypoly-late">
     <title>Important Taylor Series Expansions</title>
     <tabular>
       <row>

From 0497b5abce5cb9ed04d1ef458b44421956c0a9ce Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Thu, 4 Jun 2026 15:20:46 -0600
Subject: [PATCH 13/18] and everything else...

---
 ptx/sec_ABC.ptx                               |  11 +-
 ptx/sec_FTC.ptx                               |   2 +-
 ptx/sec_Graphical_Numerical.ptx               |  18 +-
 ptx/sec_Linear.ptx                            |  11 +-
 ptx/sec_Modeling.ptx                          |   3 +-
 ptx/sec_Separable.ptx                         |   9 +-
 ptx/sec_alt_series.ptx                        |   8 +-
 ptx/sec_antider.ptx                           |   4 +-
 ptx/sec_arc_length.ptx                        |  13 +-
 ptx/sec_center_of_mass.ptx                    |  12 +-
 ptx/sec_conic_sections.ptx                    |  76 +++--
 ptx/sec_cross_product.ptx                     |  22 +-
 ptx/sec_curvature.ptx                         |   5 +-
 ptx/sec_cylindrical_spherical.ptx             |  35 +--
 ptx/sec_cylindrical_spherical_old.ptx         |  27 +-
 ptx/sec_deriv_basic_rules.ptx                 |   4 +-
 ptx/sec_deriv_chainrule.ptx                   |   7 +-
 ptx/sec_deriv_implicit.ptx                    |  81 ++---
 ptx/sec_deriv_intro.ptx                       |   4 +-
 ptx/sec_deriv_inverse_function.ptx            |   8 +-
 ptx/sec_deriv_prodquot.ptx                    |   2 +-
 ptx/sec_differentials.ptx                     |  56 ++--
 ptx/sec_directional_derivative.ptx            |  10 +-
 ptx/sec_disk.ptx                              |   2 +-
 ptx/sec_dot_product.ptx                       |  55 ++--
 ptx/sec_double_int_polar.ptx                  |   8 +-
 ptx/sec_double_int_volume.ptx                 |  32 +-
 ptx/sec_fluid_force.ptx                       |   4 +-
 ptx/sec_graph_concavity.ptx                   |  72 ++---
 ptx/sec_graph_extreme_values.ptx              |   5 +-
 ptx/sec_graph_incr_decr.ptx                   |   2 +-
 ptx/sec_graph_sketch.ptx                      |   9 +-
 ptx/sec_greensthm.ptx                         |  14 +-
 ptx/sec_hyperbolic.ptx                        |  12 +-
 ptx/sec_improper_integration.ptx              |   5 +-
 ptx/sec_int_comp_tests.ptx                    |  11 +-
 ptx/sec_iterated_integrals.ptx                |  10 +-
 ptx/sec_limit_analytically.ptx                |   2 +-
 ptx/sec_limit_continuity.ptx                  |   2 +-
 ptx/sec_limit_intro.ptx                       |   7 +-
 ptx/sec_line_int_intro.ptx                    |  11 +-
 ptx/sec_line_int_vf.ptx                       |  11 +-
 ptx/sec_lines.ptx                             |  30 +-
 ptx/sec_multi_chain.ptx                       |   3 +-
 ptx/sec_multi_extreme_values.ptx              |  10 +-
 ptx/sec_multi_intro.ptx                       |  14 +-
 ptx/sec_multi_limit.ptx                       |   6 +-
 ptx/sec_newton.ptx                            |   4 +-
 ptx/sec_numerical_integration.ptx             |  11 +-
 ptx/sec_par_calc.ptx                          |  10 +-
 ptx/sec_param_eqs.ptx                         |  26 +-
 ptx/sec_parametric_surfaces.ptx               |  18 +-
 ptx/sec_partial_derivatives.ptx               |  12 +-
 ptx/sec_planes.ptx                            |  16 +-
 ptx/sec_polar.ptx                             |  19 +-
 ptx/sec_polarcalc.ptx                         |  12 +-
 ptx/sec_power_series.ptx                      |  11 +-
 ptx/sec_ratio_root_tests.ptx                  |   8 +-
 ptx/sec_riemann.ptx                           |   6 +-
 ptx/sec_sequences.ptx                         |  73 +++--
 ptx/sec_series.ptx                            |  14 +-
 ptx/sec_shell_method.ptx                      |   2 +-
 ptx/sec_space_coord.ptx                       |  14 +-
 ptx/sec_stokes_divergence.ptx                 |  51 +--
 ptx/sec_surface_area.ptx                      |   6 +-
 ptx/sec_surface_integral.ptx                  |   6 +-
 ptx/sec_tan_norm.ptx                          |  27 +-
 ptx/sec_taylor_poly.ptx                       |  13 +-
 ptx/sec_taylor_series.ptx                     |  20 +-
 ptx/sec_total_differential.ptx                | 294 +++++++++---------
 ptx/sec_trig_sub.ptx                          |   2 -
 ptx/sec_triple_int.ptx                        |  12 +-
 ptx/sec_vector_fields.ptx                     |   6 +-
 ptx/sec_vector_intro.ptx                      |  23 +-
 ptx/sec_vvf.ptx                               |   8 +-
 ptx/sec_vvf_calc.ptx                          |   3 +-
 ptx/sec_vvf_motion.ptx                        |  17 +-
 ptx/sec_work.ptx                              |   4 +-
 .../publication-color-print-novideo.ptx       |  10 +
 xsl/apex-latex-print-color.xsl                |   9 +-
 80 files changed, 687 insertions(+), 845 deletions(-)

diff --git a/ptx/sec_ABC.ptx b/ptx/sec_ABC.ptx
index 8368145e4..04dbe4a2f 100644
--- a/ptx/sec_ABC.ptx
+++ b/ptx/sec_ABC.ptx
@@ -939,8 +939,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the area of the shaded region in the given graph.
+            Find the area of the shaded region in the given graph.
           </p>
         </introduction>
 
@@ -1454,8 +1453,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the total area enclosed by the functions <m>f</m> and <m>g</m>.
+            Find the total area enclosed by the functions <m>f</m> and <m>g</m>.
           </p>
         </introduction>
   <!-- Exercise 11 -->
@@ -1685,7 +1683,7 @@
       <exercisegroup cols="2" xml:id="exset-area-between-two-ways">
         <introduction>
           <p>
-            In the following exercises, find the area of the enclosed region in two ways:
+            Find the area of the enclosed region in two ways:
           </p>
 
           <p>
@@ -2107,8 +2105,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the area of the triangle formed by the given three points.
+            Find the area of the triangle formed by the given three points.
           </p>
         </introduction>
   <!-- Exercise 23 -->
diff --git a/ptx/sec_FTC.ptx b/ptx/sec_FTC.ptx
index ac8f0ccb2..c36332121 100644
--- a/ptx/sec_FTC.ptx
+++ b/ptx/sec_FTC.ptx
@@ -1231,7 +1231,7 @@
           as done in <xref ref="fig_ftc6"/>.
         </p>
 
-        <figure xml:id="fig_ftc6" vshift="2">
+        <figure xml:id="fig_ftc6" vshift="0">
           <caption>Sketching the region enclosed by <m>y=x^2+x-5</m> and <m>y=3x-2</m> in <xref ref="ex_ftc6"/></caption>
           <image width="47%">
             <shortdescription>
diff --git a/ptx/sec_Graphical_Numerical.ptx b/ptx/sec_Graphical_Numerical.ptx
index 9c6f6eb02..a3b63c162 100644
--- a/ptx/sec_Graphical_Numerical.ptx
+++ b/ptx/sec_Graphical_Numerical.ptx
@@ -1806,8 +1806,7 @@
       <exercisegroup cols="2" xml:id="exset-graphical-numerical-verify-sol">
         <introduction>
           <p>
-            In the following exercises,
-            verify that the given function is a solution to the differential equation or initial value problem.
+            Verify that the given function is a solution to the differential equation or initial value problem.
           </p>
         </introduction>
 
@@ -1882,8 +1881,7 @@
       <exercisegroup cols="2" xml:id="exset-graphical-numerical-verify-particular">
         <introduction>
           <p>
-            In the following exercises,
-            verify that the given function is a solution to the differential equation and find the <m>C</m> 
+            Verify that the given function is a solution to the differential equation and find the <m>C</m> 
             value required to make the function satisfy the initial condition.
           </p>
         </introduction>
@@ -1934,8 +1932,7 @@
       <exercisegroup cols="2" xml:id="exset-graphical-numerical-sketch-slope">
         <introduction>
           <p>
-            In the following exercises,
-            sketch a slope field for the given differential equation.
+            Sketch a slope field for the given differential equation.
             Let <m>x</m> and <m>y</m> range between <m>-2</m> and <m>2</m>.
           </p>
         </introduction>
@@ -2301,8 +2298,7 @@
       <exercisegroup cols="2" xml:id="exset-graphical-numerical-sketch-sol">
         <introduction>
           <p>
-            In the following exercises,
-            sketch the slope field for the differential equation,
+            Sketch the slope field for the differential equation,
             and use it to draw a sketch of the solution to the initial value problem.
           </p>
         </introduction>
@@ -2513,8 +2509,7 @@
       <exercisegroup cols="2" xml:id="exset-graphical-numerical-euler">
         <introduction>
           <p>
-            In the following exercises,
-            use Euler's Method to make a table of values that approximates the solution to the initial value problem on the given interval.
+            Use Euler's Method to make a table of values that approximates the solution to the initial value problem on the given interval.
             Use the specified <m>h</m> or <m>N</m> value.
           </p>
         </introduction>
@@ -2641,8 +2636,7 @@
       <exercisegroup>
         <introduction>
           <p>
-            In the following exercises,
-            use the provided solution <m>y(x)</m> and Euler's Method with the <m>h=0.2</m> and <m>h=0.1</m> to complete the following table.
+            Use the provided solution <m>y(x)</m> and Euler's Method with the <m>h=0.2</m> and <m>h=0.1</m> to complete the following table.
           </p>
           <tabular>
             <col right="minor"/>
diff --git a/ptx/sec_Linear.ptx b/ptx/sec_Linear.ptx
index a6969113c..6b63fe7fc 100644
--- a/ptx/sec_Linear.ptx
+++ b/ptx/sec_Linear.ptx
@@ -280,7 +280,7 @@
     <p>
       Integrating,
       <md>
-        \ln \mu = \int p(x)\,dx
+        \ln(\mu) = \int p(x)\,dx
       </md>,
       or
       <md>
@@ -776,7 +776,7 @@
       <exercisegroup cols="2" xml:id="exset-ode-linear-general-sol">
         <introduction>
           <p>
-            In the following exercises, Find the general solution to the first order linear differential equation.
+            Find the general solution to the first order linear differential equation.
           </p>
         </introduction>
         <exercise label="ex-ode-linear-general-sol-1">
@@ -879,7 +879,7 @@
       <exercisegroup cols="2" xml:id="exset-ode-linear-particular-sol">
         <introduction>
           <p>
-            In the following exercises, Find the particular solution to the initial value problem.
+            Find the particular solution to the initial value problem.
           </p>
         </introduction>
         <exercise label="ex-ode-linear-particular-sol-1">
@@ -982,8 +982,7 @@
       <exercisegroup cols="2" xml:id="exset-ode-linear-classify">
         <introduction>
           <p>
-            In the following exercises,
-            classify the differential equation as separable,
+            Classify the differential equation as separable,
             first order linear, or both,
             and solve the initial value problem using an appropriate method.
           </p>
@@ -1040,7 +1039,7 @@
       <exercisegroup cols="2" xml:id="exset-ode-linear-slope">
         <introduction>
           <p>
-            In the following exercises, draw a slope field for the differential equation.
+            Draw a slope field for the differential equation.
             Use the slope field to predict the behavior of the solution to the initial value problem for large <m>x</m> values.
             Solve the initial value problem,
             and verify your prediction.
diff --git a/ptx/sec_Modeling.ptx b/ptx/sec_Modeling.ptx
index efd46176e..29391f743 100644
--- a/ptx/sec_Modeling.ptx
+++ b/ptx/sec_Modeling.ptx
@@ -793,8 +793,7 @@
       <exercisegroup cols="2" xml:id="exset-ode-modelling">
         <introduction>
           <p>
-            In the following exercises,
-            use the tools in the section to answer the questions presented.
+            Use the tools in the section to answer the questions presented.
           </p>
         </introduction>
         <exercise label="ex-ode-modelling-proportional">
diff --git a/ptx/sec_Separable.ptx b/ptx/sec_Separable.ptx
index 8ca6b966c..1214d24f0 100644
--- a/ptx/sec_Separable.ptx
+++ b/ptx/sec_Separable.ptx
@@ -522,8 +522,7 @@
       <exercisegroup cols="2" xml:id="exset-ode-separable-determine">
         <introduction>
           <p>
-            In the following exercises,
-            decide whether the differential equation is separable or not separable.
+            Decide whether the differential equation is separable or not separable.
             If the equation is separable, write it in separated form.
           </p>
         </introduction>
@@ -581,8 +580,7 @@
       <exercisegroup cols="2" xml:id="exset-ode-separable-general-sol">
         <introduction>
           <p>
-            In the following exercises,
-            find the general solution to the separable differential equation.
+            Find the general solution to the separable differential equation.
             Be sure to check for missing constant solutions.
           </p>
         </introduction>
@@ -686,8 +684,7 @@
       <exercisegroup cols="2" xml:id="exset-ode-separable-particular-sol">
         <introduction>
           <p>
-            In the following exercises,
-            find the particular solution to the separable initial value problem.
+            Find the particular solution to the separable initial value problem.
           </p>
         </introduction>
         <exercise label="ex-ode-separable-particular-sol-1">
diff --git a/ptx/sec_alt_series.ptx b/ptx/sec_alt_series.ptx
index fa1fa2fcc..345ee437c 100644
--- a/ptx/sec_alt_series.ptx
+++ b/ptx/sec_alt_series.ptx
@@ -994,8 +994,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            an alternating series <m>\ds \sum_{n=i}^\infty a_n</m> is given.
+            An alternating series <m>\ds \sum_{n=i}^\infty a_n</m> is given.
           </p>
 
           <p>
@@ -1588,7 +1587,7 @@
         <introduction>
           <p>
             Let <m>S_n</m> be the <m>n^{ th }</m> partial sum of a series.
-            In the following exercises a convergent alternating series is given and a value of <m>n</m>.
+            A convergent alternating series is given and a value of <m>n</m>.
             Compute <m>S_n</m> and <m>S_{n+1}</m> and use these values to find bounds on the sum of the series.
           </p>
         </introduction>
@@ -1682,8 +1681,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            a convergent alternating series is given along with its sum and a value of <m>\varepsilon</m>.
+            A convergent alternating series is given along with its sum and a value of <m>\varepsilon</m>.
             Use <xref ref="thm_alt_series_approx"/>
             to find <m>n</m> such that the
             <m>n</m>th partial sum of the series is within
diff --git a/ptx/sec_antider.ptx b/ptx/sec_antider.ptx
index 898b13852..15e7fb071 100644
--- a/ptx/sec_antider.ptx
+++ b/ptx/sec_antider.ptx
@@ -406,6 +406,8 @@
       </statement>
     </theorem>
 
+    <!-- <pagebreak-latex/> -->
+
     <exercise component="proteus" label="APEX-PROTEUS-antider-2-v1">
       <title>PROTEUS EXERCISE</title>
       <statement>
@@ -438,7 +440,7 @@
       </cardsort>
     </exercise>
 
-    <p>
+    <p xml:id="p-antider-break1">
       We highlight a few important points from <xref ref="thm_indef_alg"/>.
     </p>
     <p>
diff --git a/ptx/sec_arc_length.ptx b/ptx/sec_arc_length.ptx
index 893ec5552..0d1e2c200 100644
--- a/ptx/sec_arc_length.ptx
+++ b/ptx/sec_arc_length.ptx
@@ -441,7 +441,7 @@
       </solution>
     </example>
 
-    <exercise label="APEX-PROTEUS-arclength-1-v1" compnent="proteus">
+    <exercise label="APEX-PROTEUS-arclength-1-v1" component="proteus">
       <title>PROTEUS EXERCISE</title>
       <statement>
         <p>
@@ -1285,8 +1285,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the arc length of the function on the given interval.
+            Find the arc length of the function on the given interval.
           </p>
         </introduction>
 
@@ -1473,8 +1472,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            set up the integral to compute the arc length of the function on the given interval.
+            Set up the integral to compute the arc length of the function on the given interval.
             Do not evaluate the integral.
           </p>
         </introduction>
@@ -1584,7 +1582,7 @@
 
         <introduction>
           <p>
-            In the following exercises, use Simpson's Rule, with <m>n=4</m>,
+            Use Simpson's Rule, with <m>n=4</m>,
             to approximate the arc length of the function on the given interval.
             Note: these are the same problems as in <xref first="ex_07_04_ex_13" last="ex_07_04_ex_20" text="local">Exercises</xref>.
           </p>
@@ -1697,8 +1695,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the surface area of the described solid of revolution.
+            Find the surface area of the described solid of revolution.
           </p>
         </introduction>
 
diff --git a/ptx/sec_center_of_mass.ptx b/ptx/sec_center_of_mass.ptx
index c24eb117f..54e787a83 100644
--- a/ptx/sec_center_of_mass.ptx
+++ b/ptx/sec_center_of_mass.ptx
@@ -1462,8 +1462,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            point masses are given along a line or in the plane.
+            Point masses are given along a line or in the plane.
             Find the center of mass <m>\overline{x}</m> or <m>(\overline{x},\overline{y})</m>,
             as appropriate.
             (All masses are in grams and distances are in cm.)
@@ -1559,8 +1558,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the mass/weight of the lamina described by the region <m>R</m> in the plane and its density function <m>\delta(x,y)</m>.
+            Find the mass/weight of the lamina described by the region <m>R</m> in the plane and its density function <m>\delta(x,y)</m>.
           </p>
         </introduction>
 
@@ -1720,8 +1718,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the center of mass of the lamina described by the region <m>R</m> in the plane and its density function <m>\delta(x,y)</m>.
+            Find the center of mass of the lamina described by the region <m>R</m> in the plane and its density function <m>\delta(x,y)</m>.
           </p>
 
         <p>
@@ -1917,8 +1914,7 @@
           </p>
 
           <p>
-            In the following exercises,
-            a lamina corresponding to a planar region <m>R</m> is given with a mass of 16 units.
+            A lamina corresponding to a planar region <m>R</m> is given with a mass of 16 units.
             For each, compute <m>I_x</m>,
             <m>I_y</m> and <m>I_O</m>.
           </p>
diff --git a/ptx/sec_conic_sections.ptx b/ptx/sec_conic_sections.ptx
index c435910c6..f7b7a9992 100644
--- a/ptx/sec_conic_sections.ptx
+++ b/ptx/sec_conic_sections.ptx
@@ -197,7 +197,7 @@
       </statement>
     </definition>
 
-    <figure xml:id="fig_parabola_def" vshift="-3">
+    <figure xml:id="fig_parabola_def" vshift="-2">
       <caption>Illustrating the definition of the parabola and establishing an algebraic formula</caption>
       <!-- START figures/fig_parabola_def.tex -->
       <image width="47%">
@@ -345,7 +345,7 @@
           </md>.
         </p>
 
-        <figure xml:id="fig_conic1" vshift="6">
+        <figure xml:id="fig_conic1" vshift="2">
           <caption>The parabola described in <xref ref="ex_conic1"/></caption>
           <!-- START figures/fig_conic1.tex -->
           <image width="47%">
@@ -802,7 +802,7 @@
           Find the general equation of the ellipse graphed in <xref ref="fig_conic3"/>.
         </p>
 
-        <figure xml:id="fig_conic3" vshift="-5.5">
+        <figure xml:id="fig_conic3" vshift="-1">
           <caption>The ellipse used in <xref ref="ex_conic3"/></caption>
           <!-- START figures/fig_conic3.tex -->
           <image width="47%">
@@ -894,7 +894,7 @@
           This is all graphed in <xref ref="fig_conic4"/>
         </p>
 
-        <figure xml:id="fig_conic4" vshift="-3">
+        <figure xml:id="fig_conic4" vshift="2">
           <caption>Graphing the ellipse in <xref ref="ex_conic4"/></caption>
           <!-- START figures/fig_conic4.tex -->
           <image width="47%">
@@ -1287,7 +1287,7 @@
       <ie/>, <m>2a</m>.
     </p>
 
-    <figure xml:id="fig_hyperbola_def" vshift="3">
+    <figure xml:id="fig_hyperbola_def" vshift="4">
       <caption>Labeling the significant features of a hyperbola</caption>
       <!-- START figures/fig_hyperbola_def.tex -->
       <image width="47%">
@@ -1398,7 +1398,7 @@
         as shown in <xref ref="fig_hyperbola_asy1"/>.
       </p>
 
-      <figure xml:id="fig_hyperbola_asy1" vshift="4">
+      <figure xml:id="fig_hyperbola_asy1" vshift="5">
         <caption>Graphing the hyperbola <m>\frac{x^2}9-\frac{y^2}1 = 1</m> along with its asymptotes, <m>y=\pm x/3</m></caption>
         <!-- START figures/fig_hyperbola_asy1.tex -->
         <image width="47%">
@@ -1444,7 +1444,7 @@
         The diagonals of the rectangle lie on the asymptotes.
       </p>
 
-      <figure xml:id="fig_hyperbola_asy2" vshift="-0.5">
+      <figure xml:id="fig_hyperbola_asy2" vshift="0.5">
         <caption>Using the asymptotes of a hyperbola as a graphing aid</caption>
         <!-- START figures/fig_hyperbola_asy2.tex -->
         <image width="47%">
@@ -1694,6 +1694,9 @@
 
     <paragraphs>
       <title>Eccentricity</title>
+      <p>
+        The eccentricity of a hyperbola is defined in the same way as an ellipse.
+      </p>
       <definition xml:id="def_hyperbola_eccentricity">
         <title>Eccentricity of a Hyperbola</title>
         <statement>
@@ -1705,6 +1708,20 @@
         </statement>
       </definition>
 
+      <p>
+        Note that this is the definition of eccentricity as used for the ellipse.
+        When <m>c</m> is close in value to <m>a</m> (<ie/>, <m>e\approx 1</m>),
+        the hyperbola is very narrow
+        (looking almost like crossed lines).
+        <xref ref="fig_hyperbola_ecc"/>
+        shows hyperbolas centered at the origin with <m>a=1</m>.
+        The graph in <xref ref="fig_hyperbola_ecca"/> has <m>c=1.05</m>,
+        giving an eccentricity of <m>e=1.05</m>, which is close to 1.
+        As <m>c</m> grows larger,
+        the hyperbola widens and begins to look like parallel lines,
+        as shown in <xref ref="fig_hyperbola_eccd"/>.
+      </p>
+
       <figure xml:id="fig_hyperbola_ecc">
         <caption>Understanding the eccentricity of a hyperbola</caption>
         <sbsgroup>
@@ -1907,20 +1924,6 @@
           </sidebyside>
         </sbsgroup>
       </figure>
-
-      <p>
-        Note that this is the definition of eccentricity as used for the ellipse.
-        When <m>c</m> is close in value to <m>a</m> (<ie/>, <m>e\approx 1</m>),
-        the hyperbola is very narrow
-        (looking almost like crossed lines).
-        <xref ref="fig_hyperbola_ecc"/>
-        shows hyperbolas centered at the origin with <m>a=1</m>.
-        The graph in <xref ref="fig_hyperbola_ecca"/> has <m>c=1.05</m>,
-        giving an eccentricity of <m>e=1.05</m>, which is close to 1.
-        As <m>c</m> grows larger,
-        the hyperbola widens and begins to look like parallel lines,
-        as shown in <xref ref="fig_hyperbola_eccd"/>.
-      </p>
     </paragraphs>
 
     <paragraphs>
@@ -1992,7 +1995,7 @@
         How can the location be determined in such a situation?
       </p>
 
-      <figure xml:id="fig_hyperbola_reflect" vshift="0">
+      <figure xml:id="fig_hyperbola_reflect" vshift="-1">
         <caption>Illustrating the reflective property of a hyperbola</caption>
         <!-- START figures/fig_hyperbola_reflect.tex -->
         <image width="47%">
@@ -2361,8 +2364,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the equation of the parabola defined by the given information.
+            Find the equation of the parabola defined by the given information.
             Sketch the parabola.
           </p>
         </introduction>
@@ -2508,8 +2510,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            the equation of a parabola and a point on its graph are given.
+            The equation of a parabola and a point on its graph are given.
             Find the focus and directrix of the parabola,
             and verify that the given point is equidistant from the focus and directrix.
           </p>
@@ -2556,7 +2557,7 @@
 
         <introduction>
           <p>
-            In the following exercises, sketch the ellipse defined by the given equation.
+            Sketch the ellipse defined by the given equation.
             Label the center, foci and vertices.
           </p>
         </introduction>
@@ -2594,8 +2595,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the equation of the ellipse shown in the graph.
+            Find the equation of the ellipse shown in the graph.
             Give the location of the foci and the eccentricity of the ellipse.
           </p>
         </introduction>
@@ -2700,8 +2700,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the equation of the ellipse defined by the given information.
+            Find the equation of the ellipse defined by the given information.
             Sketch the elllipse.
           </p>
         </introduction>
@@ -2781,8 +2780,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            write the equation of the given ellipse in standard form.
+            Write the equation of the given ellipse in standard form.
           </p>
         </introduction>
 
@@ -2859,8 +2857,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the equation of the hyperbola shown in the graph.
+            Find the equation of the hyperbola shown in the graph.
           </p>
         </introduction>
 
@@ -3081,8 +3078,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            sketch the hyperbola defined by the given equation.
+            Sketch the hyperbola defined by the given equation.
             Label the center and foci.
           </p>
         </introduction>
@@ -3120,8 +3116,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the equation of the hyperbola defined by the given information.
+            Find the equation of the hyperbola defined by the given information.
             Sketch the hyperbola.
           </p>
         </introduction>
@@ -3201,8 +3196,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            write the equation of the hyperbola in standard form.
+            Write the equation of the hyperbola in standard form.
           </p>
         </introduction>
 
diff --git a/ptx/sec_cross_product.ptx b/ptx/sec_cross_product.ptx
index dbd6f53cf..f39326016 100644
--- a/ptx/sec_cross_product.ptx
+++ b/ptx/sec_cross_product.ptx
@@ -383,7 +383,7 @@
     </theorem>
 
     <aside xml:id="aside-cross-orthogonal" vshift="4">
-      <title>Parallel vectors and the cross product</title>
+      <title>The cross product and parallel vectors</title>
 
       <p>
         We could rewrite <xref ref="def_orthogonal"/>
@@ -1495,7 +1495,7 @@
 
         <introduction>
           <p>
-            In the following exercises, vectors <m>\vec u</m> and <m>\vec v</m> are given.
+            Vectors <m>\vec u</m> and <m>\vec v</m> are given.
             Compute <m>\vec u\times\vec v</m> and check that this vector is orthogonal to both <m>\vec u</m> and <m>\vec v</m>.
           </p>
         </introduction>
@@ -1744,8 +1744,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            the magnitudes of vectors <m>\vec u</m> and <m>\vec v</m> in <m>\mathbb{R}^3</m> are given,
+            The magnitudes of vectors <m>\vec u</m> and <m>\vec v</m> in <m>\mathbb{R}^3</m> are given,
             along with the angle <m>\theta</m> between them.
             Use this information to find the magnitude of <m>\vec u\times\vec v</m>.
           </p>
@@ -1824,8 +1823,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the area of the parallelogram defined by the given vectors.
+            Find the area of the parallelogram defined by the given vectors.
           </p>
         </introduction>
 
@@ -1914,8 +1912,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the area of the triangle with the given vertices.
+            Find the area of the triangle with the given vertices.
           </p>
         </introduction>
 
@@ -2004,8 +2001,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the area of the quadrilateral with the given vertices.
+            Find the area of the quadrilateral with the given vertices.
             (Hint: break the quadrilateral into two triangles.)
           </p>
         </introduction>
@@ -2066,8 +2062,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the volume of the parallelepiped defined by the given vectors.
+            Find the volume of the parallelepiped defined by the given vectors.
           </p>
         </introduction>
 
@@ -2114,8 +2109,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find a unit vector orthogonal to both <m>\vec u</m> and <m>\vec v</m>.
+            Find a unit vector orthogonal to both <m>\vec u</m> and <m>\vec v</m>.
           </p>
         </introduction>
 
diff --git a/ptx/sec_curvature.ptx b/ptx/sec_curvature.ptx
index 47c9c6422..cce5f883c 100644
--- a/ptx/sec_curvature.ptx
+++ b/ptx/sec_curvature.ptx
@@ -1301,7 +1301,7 @@
 
         <introduction>
           <p>
-            In the following exercises, a position function <m>\vrt</m> is given,
+            A position function <m>\vrt</m> is given,
             where <m>t=0</m> corresponds to the initial position.
             Find the arc length parameter <m>s</m>,
             and rewrite <m>\vrt</m> in terms of <m>s</m>;
@@ -1410,8 +1410,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            a curve <m>C</m> is described along with 2 points on <m>C</m>.
+            A curve <m>C</m> is described along with 2 points on <m>C</m>.
           </p>
 
           <p>
diff --git a/ptx/sec_cylindrical_spherical.ptx b/ptx/sec_cylindrical_spherical.ptx
index 83b9ce403..08a7319bb 100644
--- a/ptx/sec_cylindrical_spherical.ptx
+++ b/ptx/sec_cylindrical_spherical.ptx
@@ -236,7 +236,7 @@
           This plane is the same as the plane described by <m>z=2</m> in rectangular coordinates.
         </p>
 
-        <figure xml:id="fig_cylindrical1" vshift="-2">
+        <figure xml:id="fig_cylindrical1" vshift="0">
           <caption>Graphing the canonical surfaces in cylindrical coordinates from <xref ref="ex_cylindrical1"/></caption>
           <image width="47%">
             <shortdescription>Three surfaces in space, corresponding to fixed values of each of the three cylindrical coordinates.</shortdescription>
@@ -927,8 +927,8 @@
       The following Key Idea gives conversions to/from our three spatial coordinate systems.
     </p>
 
-    <!-- <insight xml:id="idea_convert_coords" hstretch="330" hskip="60"> -->
-    <insight xml:id="idea_convert_coords" hstretch="330">
+    <insight xml:id="idea_convert_coords" hstretch="330" hskip="60">
+    <!-- <insight xml:id="idea_convert_coords" hstretch="330"> -->
       <title>Converting Between Rectangular, Cylindrical and Spherical Coordinates</title>
       <p>
         <ul>
@@ -1811,8 +1811,7 @@
       <exercisegroup cols="2" xml:id="exset-cylindrical-spherical-convert">
         <introduction>
           <p>
-            In the following exercises,
-            points are given in either the rectangular,
+            Points are given in either the rectangular,
             cylindrical or spherical coordinate systems.
             Find the coordinates of the points in the other systems.
           </p>
@@ -1939,7 +1938,7 @@
       <exercisegroup cols="2" xml:id="exset-cylindrical-region">
         <introduction>
           <p>
-            In the following exercises, describe the curve,
+            Describe the curve,
             surface or region in space determined by the given bounds in cylindrical coordinates.
           </p>
         </introduction>
@@ -2009,7 +2008,7 @@
       <exercisegroup cols="2" xml:id="exset-spherical-region">
         <introduction>
           <p>
-            In the following exercises, describe the curve,
+            Describe the curve,
             surface or region in space determined by the given bounds in spherical coordinates.
           </p>
         </introduction>
@@ -2084,7 +2083,7 @@
       <exercisegroup cols="2" xml:id="exset-cylindrical-spherical-setup">
         <introduction>
           <p>
-            In the following exercises, standard regions in space,
+            Standard regions in space,
             as defined by cylindrical and spherical coordinates, are shown.
             Set up the triple integral that integrates the given function over the graphed region.
           </p>
@@ -2446,8 +2445,7 @@ draw(arc((0,0,0),.8*(r1*cos(t1)*sin(p2),r1*sin(t1)*sin(p2),0),.7*(r1*cos(t1)*sin
       <exercisegroup cols="2" xml:id="exset-cylindrical-integral-region">
         <introduction>
           <p>
-            In the following exercises,
-            a triple integral in cylindrical coordinates is given.
+            A triple integral in cylindrical coordinates is given.
             Describe the region in space defined by the bounds of the integral.
           </p>
         </introduction>
@@ -2553,8 +2551,7 @@ draw(arc((0,0,0),.8*(r1*cos(t1)*sin(p2),r1*sin(t1)*sin(p2),0),.7*(r1*cos(t1)*sin
       <exercisegroup cols="2" xml:id="exset-spherical-integral-region">
         <introduction>
           <p>
-            In the following exercises,
-            a triple integral in spherical coordinates is given.
+            A triple integral in spherical coordinates is given.
             Describe the region in space defined by the bounds of the integral.
           </p>
         </introduction>
@@ -2663,8 +2660,7 @@ draw(arc((0,0,0),.8*(r1*cos(t1)*sin(p2),r1*sin(t1)*sin(p2),0),.7*(r1*cos(t1)*sin
       <exercisegroup cols="2" xml:id="exset-cylindrical-mass">
         <introduction>
           <p>
-            In the following exercises,
-            a solid is described along with its density function.
+            A solid is described along with its density function.
             Find the mass of the solid using cylindrical coordinates.
           </p>
         </introduction>
@@ -2745,8 +2741,7 @@ draw(arc((0,0,0),.8*(r1*cos(t1)*sin(p2),r1*sin(t1)*sin(p2),0),.7*(r1*cos(t1)*sin
       <exercisegroup cols="2" xml:id="exset-cylindrical-center-mass">
         <introduction>
           <p>
-            In the following exercises,
-            a solid is described along with its density function.
+            A solid is described along with its density function.
             Find the center of mass of the solid using cylindrical coordinates.
             (Note: these are the same solids and density functions as found in <xref first="ex_13_07_ex_23" last="ex_13_07_ex_26" text="local">Exercises</xref>.)
           </p>
@@ -2851,8 +2846,7 @@ draw(arc((0,0,0),.8*(r1*cos(t1)*sin(p2),r1*sin(t1)*sin(p2),0),.7*(r1*cos(t1)*sin
       <exercisegroup cols="2" xml:id="exset-spherical-mass">
         <introduction>
           <p>
-            In the following exercises,
-            a solid is described along with its density function.
+            A solid is described along with its density function.
             Find the mass of the solid using spherical coordinates.
           </p>
         </introduction>
@@ -2937,8 +2931,7 @@ draw(arc((0,0,0),.8*(r1*cos(t1)*sin(p2),r1*sin(t1)*sin(p2),0),.7*(r1*cos(t1)*sin
       <exercisegroup cols="2" xml:id="exset-spherical-center-mass">
         <introduction>
           <p>
-            In the following exercises,
-            a solid is described along with its density function.
+            A solid is described along with its density function.
             Find the center of mass of the solid using spherical coordinates.
             (Note: these are the same solids and density functions as found in <xref first="ex_13_07_ex_31" last="ex_13_07_ex_34" text="local">Exercises</xref>.)
           </p>
@@ -3045,7 +3038,7 @@ draw(arc((0,0,0),.8*(r1*cos(t1)*sin(p2),r1*sin(t1)*sin(p2),0),.7*(r1*cos(t1)*sin
       <exercisegroup cols="2" xml:id="exset-cylindrical-spherical-integral-compare">
         <introduction>
           <p>
-            In the following exercises, a region is space is described.
+            A region is space is described.
             Set up the triple integrals that find the volume of this region using rectangular,
             cylindrical and spherical coordinates,
             then comment on which of the three appears easiest to evaluate.
diff --git a/ptx/sec_cylindrical_spherical_old.ptx b/ptx/sec_cylindrical_spherical_old.ptx
index c40ff3fd2..22a766f95 100644
--- a/ptx/sec_cylindrical_spherical_old.ptx
+++ b/ptx/sec_cylindrical_spherical_old.ptx
@@ -1746,8 +1746,7 @@
       <exercisegroup cols="2">
         <introduction>
           <p>
-            In the following exercises,
-            points are given in either the rectangular,
+            Points are given in either the rectangular,
             cylindrical or spherical coordinate systems.
             Find the coordinates of the points in the other systems.
           </p>
@@ -1896,7 +1895,7 @@
       <exercisegroup cols="2">
         <introduction>
           <p>
-            In the following exercises, describe the curve,
+            Describe the curve,
             surface or region in space determined by the given bounds.
           </p>
         </introduction>
@@ -2055,7 +2054,7 @@
       <exercisegroup cols="2">
         <introduction>
           <p>
-            In the following exercises, standard regions in space,
+            Standard regions in space,
             as defined by cylindrical and spherical coordinates, are shown.
             Set up the triple integral that integrates the given function over the graphed region.
           </p>
@@ -2403,8 +2402,7 @@
       <exercisegroup cols="2">
         <introduction>
           <p>
-            In the following exercises,
-            a triple integral in cylindrical coordinates is given.
+            A triple integral in cylindrical coordinates is given.
             Describe the region in space defined by the bounds of the integral.
           </p>
         </introduction>
@@ -2510,8 +2508,7 @@
       <exercisegroup cols="2">
         <introduction>
           <p>
-            In the following exercises,
-            a triple integral in spherical coordinates is given.
+            A triple integral in spherical coordinates is given.
             Describe the region in space defined by the bounds of the integral.
           </p>
         </introduction>
@@ -2620,8 +2617,7 @@
       <exercisegroup cols="2">
         <introduction>
           <p>
-            In the following exercises,
-            a solid is described along with its density function.
+            A solid is described along with its density function.
             Find the mass of the solid using cylindrical coordinates.
           </p>
         </introduction>
@@ -2702,8 +2698,7 @@
       <exercisegroup cols="2">
         <introduction>
           <p>
-            In the following exercises,
-            a solid is described along with its density function.
+            A solid is described along with its density function.
             Find the center of mass of the solid using cylindrical coordinates.
             (Note: these are the same solids and density functions as found in <xref first="ex_13_07_ex_23" last="ex_13_07_ex_26" text="local">Exercises</xref>.)
           </p>
@@ -2808,8 +2803,7 @@
       <exercisegroup cols="2">
         <introduction>
           <p>
-            In the following exercises,
-            a solid is described along with its density function.
+            A solid is described along with its density function.
             Find the mass of the solid using spherical coordinates.
           </p>
         </introduction>
@@ -2894,8 +2888,7 @@
       <exercisegroup cols="2">
         <introduction>
           <p>
-            In the following exercises,
-            a solid is described along with its density function.
+            A solid is described along with its density function.
             Find the center of mass of the solid using spherical coordinates.
             (Note: these are the same solids and density functions as found in <xref first="ex_13_07_ex_31" last="ex_13_07_ex_34" text="local">Exercises</xref>.)
           </p>
@@ -3002,7 +2995,7 @@
       <exercisegroup cols="2">
         <introduction>
           <p>
-            In the following exercises, a region is space is described.
+            A region in space is described.
             Set up the triple integrals that find the volume of this region using rectangular,
             cylindrical and spherical coordinates,
             then comment on which of the three appears easiest to evaluate.
diff --git a/ptx/sec_deriv_basic_rules.ptx b/ptx/sec_deriv_basic_rules.ptx
index e1bc416a7..cf44179a1 100644
--- a/ptx/sec_deriv_basic_rules.ptx
+++ b/ptx/sec_deriv_basic_rules.ptx
@@ -159,7 +159,7 @@
   </p>
 
   <p xml:id="vidint-deriv_basic_rules_exp_func" component="video">
-    <xref ref="thm_deriv_common"/> states that the natural exponential function has a remarkable propery:
+    <xref ref="thm_deriv_common"/> states that the natural exponential function has a remarkable property:
     it is equal to its own derivative! The video in <xref ref="vid_deriv_basic_rules_exp_func"/> explains why this is the case.
   </p>
 
@@ -304,6 +304,8 @@
     (the third is answered in the next section).
   </p>
 
+  <enlarge-page skipsize="2"/>
+
   <theorem xml:id="thm_deriv_prop">
     <title>Properties of the Derivative</title>
     <statement>
diff --git a/ptx/sec_deriv_chainrule.ptx b/ptx/sec_deriv_chainrule.ptx
index 2bddf0241..8265ac15b 100644
--- a/ptx/sec_deriv_chainrule.ptx
+++ b/ptx/sec_deriv_chainrule.ptx
@@ -461,7 +461,7 @@
       </p>
 
       <p>
-        <dl>
+        <ul>
           <li>
             <title><m>F_1(x) = (1-x)^2</m></title>
             <p>
@@ -519,7 +519,7 @@
               </md>.
             </p>
           </li>
-        </dl>
+        </ul>
       </p>
     </solution>
   </example>
@@ -2007,6 +2007,7 @@
           <p>
             Find the equations of tangent and normal lines to the graph of the function at the given point.
             Note: the functions here are the same as in <xref first="exer_02_05_06" last="exer_02_05_09" text="local">Exercises</xref>.
+              <enlarge-page skipsize="2"/>
           </p>
         </introduction>
 
@@ -2130,8 +2131,6 @@
         </exercise>
       </exercisegroup>
 
-      <enlarge-page skipsize="2"/>
-
       <exercise label="ex-deriv-chain-tangent-5">
         <webwork xml:id="webwork-ex-deriv-chain-tangent-5">
           <pg-code>
diff --git a/ptx/sec_deriv_implicit.ptx b/ptx/sec_deriv_implicit.ptx
index b1a35647a..252a9827c 100644
--- a/ptx/sec_deriv_implicit.ptx
+++ b/ptx/sec_deriv_implicit.ptx
@@ -1872,55 +1872,42 @@
         </exercise>
       </exercisegroup>
 
-      <exercise label="ex-deriv-implicit-compute-14">
-        <webwork xml:id="webwork-ex-deriv-implicit-compute-14">
-          <introduction>
+      <exercisegroup cols="2" xml:id="ex-deriv-implicit-compute-14">
+        <introduction>
+          <p>
+            Show that <m>\lz{y}{x}</m> is the same for each of the following implicitly defined functions.
+          </p>
+        </introduction>
+
+        <exercise label="ex-deriv-implicit-compare-a">
+          <statement>
             <p>
-              Show that <m>\lz{y}{x}</m> is the same for each of the following implicitly defined functions.
+              <m>xy=1</m>
             </p>
-            </introduction>
-            <task label="ex-deriv-implicit-compare-a">
-              <statement>
-                <p>
-                  <m>xy=1</m>
-                </p>
-                <p>
-                  <var form="essay"/>
-                </p>
-              </statement>
-            </task>
-            <task label="ex-deriv-implicit-compare-b">
-              <statement>
-                <p>
-                  <m>x^2y^2=1</m>
-                </p>
-                <p>
-                  <var form="essay"/>
-                </p>
-              </statement>
-            </task>
-            <task label="ex-deriv-implicit-compare-c">
-              <statement>
-                <p>
-                  <m>\sin(xy) = 1</m>
-                </p>
-                <p>
-                  <var form="essay"/>
-                </p>
-              </statement>
-            </task>
-            <task label="ex-deriv-implicit-compare-d">
-              <statement>
-                <p>
-                  <m>\ln(xy) =1</m>
-                </p>
-                <p>
-                  <var form="essay"/>
-                </p>
-              </statement>
-            </task>
-        </webwork>
-      </exercise>
+          </statement>
+        </exercise>
+        <exercise label="ex-deriv-implicit-compare-b">
+          <statement>
+            <p>
+              <m>x^2y^2=1</m>
+            </p>
+          </statement>
+        </exercise>
+        <exercise label="ex-deriv-implicit-compare-c">
+          <statement>
+            <p>
+              <m>\sin(xy) = 1</m>
+            </p>
+          </statement>
+        </exercise>
+        <exercise label="ex-deriv-implicit-compare-d">
+          <statement>
+            <p>
+              <m>\ln(xy) =1</m>
+            </p>
+          </statement>
+        </exercise>
+      </exercisegroup>
 
       <!-- TODO: solutions for this exercise group. Answers are in APEX -->
       <exercisegroup cols="2" xml:id="exset-deriv-implicit-tangent">
diff --git a/ptx/sec_deriv_intro.ptx b/ptx/sec_deriv_intro.ptx
index 263795376..a3db3fd70 100644
--- a/ptx/sec_deriv_intro.ptx
+++ b/ptx/sec_deriv_intro.ptx
@@ -495,7 +495,7 @@
           along with the tangent lines at <m>x=1</m> and <m>x=3</m>.
         </p>
 
-        <figure xml:id="fig_tangent1" vshift="3">
+        <figure xml:id="fig_tangent1" vshift="-1">
           <caption>A graph of <m>f(x) = 3x^2+5x-7</m> and its tangent lines at <m>x=1</m> and <m>x=3</m></caption>
           <!-- START figures/fig_tangent1.tex -->
           <image width="47%">
@@ -1670,7 +1670,7 @@
           again, this limit is easier to evluate than the limit of the difference quotient.
         </p>
 
-        <figure xml:id="fig_diff_closed1" vshift="2">
+        <figure xml:id="fig_diff_closed1" vshift="0">
           <caption>A graph of <m>y=x^{1/2}</m> and <m>y=x^{3/2}</m> in <xref ref="ex_diff_closed1"/></caption>
           <image width="47%">
             <shortdescription>
diff --git a/ptx/sec_deriv_inverse_function.ptx b/ptx/sec_deriv_inverse_function.ptx
index 7a5793bbc..f9bff723e 100644
--- a/ptx/sec_deriv_inverse_function.ptx
+++ b/ptx/sec_deriv_inverse_function.ptx
@@ -734,9 +734,10 @@
     intended to be a reference for further work.
   </p>
 
-  <pagebreak-latex/>
+  <!-- <pagebreak-latex/> -->
   
-  <theorem xml:id="thm_deriv_glossary" hstretch="420" hskip="120">
+  <!-- <theorem xml:id="thm_deriv_glossary" hstretch="420" hskip="120"> -->
+  <theorem xml:id="thm_deriv_glossary" hstretch="420">
     <title>Glossary of Derivatives of Elementary Functions</title>
     <statement>
       <p>
@@ -1431,13 +1432,12 @@
           </webwork>
         </exercise>
       </exercisegroup>
-
-      <enlarge-page skipsize="2"/>
       
       <exercisegroup cols="2" xml:id="exset-deriv-inverse-two-ways">
         <introduction>
           <p>
             Compute the derivative of the given function in two ways:
+            <enlarge-page skipsize="2"/>
             <ol cols="2">
               <li>
                 <p>
diff --git a/ptx/sec_deriv_prodquot.ptx b/ptx/sec_deriv_prodquot.ptx
index f937997a0..b9cdeecab 100644
--- a/ptx/sec_deriv_prodquot.ptx
+++ b/ptx/sec_deriv_prodquot.ptx
@@ -191,7 +191,7 @@
       then do some regrouping as shown.
     </p>
 
-    <aside xml:id="aside-derivative-add-zero" vshift="0">
+    <aside xml:id="aside-derivative-add-zero" vshift="1">
       <p>
         Adding <m>0</m> in some clever form is a common mathematical proof technique.
       </p>
diff --git a/ptx/sec_differentials.ptx b/ptx/sec_differentials.ptx
index e16fc05f3..fd7007e02 100644
--- a/ptx/sec_differentials.ptx
+++ b/ptx/sec_differentials.ptx
@@ -1921,33 +1921,7 @@
             </task>
           </webwork>
         </exercise>
-        <!-- Exercise 37: Compare errors in wall measurements from previous exercises -->
-        <exercise label="ex-differentials-survey-4">
-          <webwork xml:id="webwork-ex-differentials-survey-4">
-            <pg-macros>
-              <macro-file>parserPopUp.pl</macro-file>
-            </pg-macros>
-            <pg-code>
-              $buttons = DropDown(
-                [
-                  'Right triangle at 25 feet',
-                  'Right triangle at 100 feet',
-                  'Isosceles triangle at 50 feet',
-                ],2,showInStatic=&gt;0);
-            </pg-code>
-            <statement>
-              <p>
-                The length of the walls in
-                <xref first="exer_04_04_ex_35" last="exer_04_04_ex_37"/>
-                are essentially the same.
-                Which setup gives the most accurate result?
-              </p>
-              <p>
-                <var name="$buttons" form="buttons"/>
-              </p>
-            </statement>
-          </webwork>
-        </exercise>
+
         <!-- Exercise 38: Length of wall if the distance has the error instead of the angle -->
         <exercise label="ex-differentials-survey-5">
            <webwork xml:id="webwork-ex-differentials-survey-5">
@@ -1998,6 +1972,34 @@
             </statement>
           </webwork>
         </exercise>
+
+      <!-- Exercise 37: Compare errors in wall measurements from previous exercises -->
+        <exercise label="ex-differentials-survey-4">
+          <webwork xml:id="webwork-ex-differentials-survey-4">
+            <pg-macros>
+              <macro-file>parserPopUp.pl</macro-file>
+            </pg-macros>
+            <pg-code>
+              $buttons = DropDown(
+                [
+                  'Right triangle at 25 feet',
+                  'Right triangle at 100 feet',
+                  'Isosceles triangle at 50 feet',
+                ],2,showInStatic=&gt;0);
+            </pg-code>
+            <statement>
+              <p>
+                The length of the walls in
+                <xref first="exer_04_04_ex_35" last="exer_04_04_ex_37"/>
+                are essentially the same.
+                Which setup gives the most accurate result?
+              </p>
+              <p>
+                <var name="$buttons" form="buttons"/>
+              </p>
+            </statement>
+          </webwork>
+        </exercise>
       </exercisegroup>
     </subexercises>
   </exercises>
diff --git a/ptx/sec_directional_derivative.ptx b/ptx/sec_directional_derivative.ptx
index c4e6334aa..f2aee06b6 100644
--- a/ptx/sec_directional_derivative.ptx
+++ b/ptx/sec_directional_derivative.ptx
@@ -1367,7 +1367,7 @@
 
         <introduction>
           <p>
-            In the following exercises, a function <m>f(x,y)</m> is given.
+            A function <m>f(x,y)</m> is given.
             Find <m>\nabla f</m>.
           </p>
         </introduction>
@@ -1485,8 +1485,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            a function <m>f(x,y)</m> and a point <m>P</m> are given.
+            A function <m>f(x,y)</m> and a point <m>P</m> are given.
             Find the directional derivative of <m>f</m> in the indicated directions.
             Note: these are the same functions as in <xref first="x12_05_ex_07" last="x12_05_ex_22">Exercises</xref>.
           </p>
@@ -1771,8 +1770,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            a function <m>f(x,y)</m> and a point <m>P</m> are given.
+            A function <m>f(x,y)</m> and a point <m>P</m> are given.
             Investigate the directions of maximal increase and decrease, as indicated.
           </p>
 
@@ -2239,7 +2237,7 @@
 
         <introduction>
           <p>
-            In the following exercises, a function <m>F(x,y,z)</m>,
+            A function <m>F(x,y,z)</m>,
             a vector <m>\vec v</m> and a point <m>P</m> are given.
           </p>
 
diff --git a/ptx/sec_disk.ptx b/ptx/sec_disk.ptx
index 03df53791..45ca43cda 100644
--- a/ptx/sec_disk.ptx
+++ b/ptx/sec_disk.ptx
@@ -272,7 +272,7 @@
         the volume of this slice would then be about <m>36\Delta x_i</m> <quantity><mag/><unit base="inch" exp="3"/></quantity>.
       </p>
 
-      <pagebreak-latex/>
+      <!-- <pagebreak-latex/> -->
       
       <figure xml:id="fig_disk0a" vshift="-2.5">
         <caption>Cutting a slice in the pyramid in <xref ref="ex_disk0"/> at <m>x=3</m></caption>
diff --git a/ptx/sec_dot_product.ptx b/ptx/sec_dot_product.ptx
index e6073033e..d868f4157 100644
--- a/ptx/sec_dot_product.ptx
+++ b/ptx/sec_dot_product.ptx
@@ -533,7 +533,7 @@
           Find the angle between each pair of vectors.
         </p>
 
-        <pagebreak-latex/>
+        <!-- <pagebreak-latex/> -->
         
         <figure xml:id="fig_dotp3" vshift="-1.5">
           <caption>Vectors used in <xref ref="ex_dotp3"/></caption>
@@ -1814,7 +1814,7 @@
 
         <introduction>
           <p>
-            In the following exercises, find the dot product of the given vectors.
+            Find the dot product of the given vectors.
           </p>
         </introduction>
 
@@ -1976,8 +1976,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the measure of the angle between the two vectors in radians.
+            Find the measure of the angle between the two vectors in radians.
           </p>
         </introduction>
 
@@ -2066,7 +2065,7 @@
 
         <introduction>
           <p>
-            In the following exercises, a vector <m>\vec v</m> is given.
+            A vector <m>\vec v</m> is given.
             Give two vectors that are orthogonal to <m>\vec v</m>.
           </p>
         </introduction>
@@ -2240,7 +2239,7 @@
 
         <introduction>
           <p>
-            In the following exercises, vectors <m>\vec u</m> and <m>\vec v</m> are given.
+            Vectors <m>\vec u</m> and <m>\vec v</m> are given.
             Find <m>\proj uv</m>,
             the orthogonal projection of <m>\vec u</m> onto <m>\vec v</m>,
             and sketch all three vectors with the same initial point.
@@ -2407,7 +2406,7 @@
 
         <introduction>
           <p>
-            In the following exercises, vectors <m>\vec u</m> and <m>\vec v</m> are given.
+            Vectors <m>\vec u</m> and <m>\vec v</m> are given.
             Write <m>\vec u</m> as the sum of two vectors,
             one of which is parallel to <m>\vec v</m>
             (or is zero)
@@ -2473,13 +2472,10 @@
 
               <statement>
                 <p>
-                  Write <m>\vec u = \la 1,2\ra</m> as the sum of two vectors,
-                  one parallel to <m>\vec v = \la -1,3\ra</m>
-                  (or zero)
-                  and the other perpendicular.
+                  <m>\vec u = \la 1,2\ra</m>and <m>\vec v = \la -1,3\ra</m>.
                 </p>
 
-                <p>
+                <p component="web">
                   <m>\vec u=</m><var name="$multians" width="15"/><m>{}+{}</m><var name="$multians" width="15"/>
                 </p>
               </statement>
@@ -2543,13 +2539,10 @@
 
               <statement>
                 <p>
-                  Write <m>\vec u = \la 5,5\ra</m> as the sum of two vectors,
-                  one parallel to <m>\vec v = \la 1,3\ra</m>
-                  (or zero)
-                  and the other perpendicular.
+                  <m>\vec u = \la 5,5\ra</m> and <m>\vec v = \la 1,3\ra</m>.
                 </p>
 
-                <p>
+                <p component="web">
                   <m>\vec u=</m><var name="$multians" width="15"/><m>{}+{}</m><var name="$multians" width="15"/>
                 </p>
               </statement>
@@ -2613,13 +2606,10 @@
 
               <statement>
                 <p>
-                  Write <m>\vec u = \la -3,2\ra</m> as the sum of two vectors,
-                  one parallel to <m>\vec v = \la 1,1\ra</m>
-                  (or zero)
-                  and the other perpendicular.
+                  <m>\vec u = \la -3,2\ra</m> and <m>\vec v = \la 1,1\ra</m>.
                 </p>
 
-                <p>
+                <p component="web">
                   <m>\vec u=</m><var name="$multians" width="15"/><m>{}+{}</m><var name="$multians" width="15"/>
                 </p>
               </statement>
@@ -2683,13 +2673,10 @@
 
               <statement>
                 <p>
-                  Write <m>\vec u = \la -3,2\ra</m> as the sum of two vectors,
-                  one parallel to <m>\vec v = \la 2,3\ra</m>
-                  (or zero)
-                  and the other perpendicular.
+                  <m>\vec u = \la -3,2\ra</m> and <m>\vec v = \la 2,3\ra</m>.
                 </p>
 
-                <p>
+                <p component="web">
                   <m>\vec u=</m><var name="$multians" width="15"/><m>{}+{}</m><var name="$multians" width="15"/>
                 </p>
               </statement>
@@ -2753,13 +2740,10 @@
 
               <statement>
                 <p>
-                  Write <m>\vec u = \la 1,5,1\ra</m> as the sum of two vectors,
-                  one parallel to <m>\vec v = \la 1,2,3\ra</m>
-                  (or zero)
-                  and the other perpendicular.
+                  <m>\vec u = \la 1,5,1\ra</m> and <m>\vec v = \la 1,2,3\ra</m>.
                 </p>
 
-                <p>
+                <p component="web">
                   <m>\vec u=</m><var name="$multians" width="15"/><m>{}+{}</m><var name="$multians" width="15"/>
                 </p>
               </statement>
@@ -2823,13 +2807,10 @@
 
               <statement>
                 <p>
-                  Write <m>\vec u = \la 3,-1,2\ra</m> as the sum of two vectors,
-                  one parallel to <m>\vec v = \la 2,2,1\ra</m>
-                  (or zero)
-                  and the other perpendicular.
+                  <m>\vec u = \la 3,-1,2\ra</m> and <m>\vec v = \la 2,2,1\ra</m>.
                 </p>
 
-                <p>
+                <p component="web">
                   <m>\vec u=</m><var name="$multians" width="15"/><m>{}+{}</m><var name="$multians" width="15"/>
                 </p>
               </statement>
diff --git a/ptx/sec_double_int_polar.ptx b/ptx/sec_double_int_polar.ptx
index c6a4dfcdf..2936308d8 100644
--- a/ptx/sec_double_int_polar.ptx
+++ b/ptx/sec_double_int_polar.ptx
@@ -779,7 +779,7 @@
         Find the volume of the solid.
       </p>
 
-      <figure xml:id="fig_doublepol4" vshift="0">
+      <figure xml:id="fig_doublepol4" vshift="-1">
         <caption>Visualizing the solid used in <xref ref="ex_doublepol4"/></caption>
 
         <!-- START figures/figdoublepol4_3D.asy -->
@@ -1277,12 +1277,12 @@
         </exercise>
 
       </exercisegroup>
-      <exercisegroup cols="2">
+
+      <exercisegroup cols="2" xml:id="exset-double-polar-special">
 
         <introduction>
           <p>
-            In the following exercises,
-            special double integrals are presented that are especially well suited for evaluation in polar coordinates.
+            The next two exercises present special double integrals that are especially well suited for evaluation in polar coordinates.
           </p>
         </introduction>
 
diff --git a/ptx/sec_double_int_volume.ptx b/ptx/sec_double_int_volume.ptx
index fc9cfb30a..d3be2e830 100644
--- a/ptx/sec_double_int_volume.ptx
+++ b/ptx/sec_double_int_volume.ptx
@@ -456,13 +456,6 @@
     </md>.
   </p>
 
-  <p>
-    Remember that though the integrand contains <m>x</m>,
-    we are viewing <m>x</m> as fixed.
-    Also note that the bounds of integration are functions of <m>x</m>:
-    the bounds depend on the value of <m>x</m>.
-  </p>
-
   <figure xml:id="fig_double_intro3" vshift="2">
     <caption>Finding volume under a surface by sweeping out a cross-sectional area</caption>
 
@@ -552,6 +545,13 @@
     <!-- figures/figdouble_intro3_3D.asy END -->
   </figure>
 
+  <p>
+    Remember that though the integrand contains <m>x</m>,
+    we are viewing <m>x</m> as fixed.
+    Also note that the bounds of integration are functions of <m>x</m>:
+    the bounds depend on the value of <m>x</m>.
+  </p>
+
   <p>
     As <m>A(x)</m> is a cross-sectional area function,
     we can find the signed volume <m>V</m> under <m>f</m> by integrating it:
@@ -632,7 +632,7 @@
         which is the rectangle with corners <m>(3,1)</m> and <m>(4,2)</m> pictured in <xref ref="fig_double1"/>,
         using Fubini's Theorem and both orders of integration.
       </p>
-      <figure xml:id="fig_double1" vshift="0">
+      <figure xml:id="fig_double1" vshift="-1">
         <caption>Finding the signed volume under a surface in <xref ref="ex_double1"/></caption>
 
         <!-- START figures/figdouble1_3D.asy -->
@@ -754,7 +754,7 @@
         <m>y=0</m> and <m>x/2+y=1</m>,
         as shown in <xref ref="fig_double2"/>.
       </p>
-      <figure xml:id="fig_double2" vshift="0">
+      <figure xml:id="fig_double2" vshift="-2">
         <caption>Finding the signed volume under the surface in <xref ref="ex_double2"/></caption>
 
         <!-- START figures/figdouble2_3D.asy -->
@@ -962,7 +962,7 @@
               </md>.
             </p>
 
-            <figure xml:id="fig_double_region" vshift="12">
+            <figure xml:id="fig_double_region" vshift="7">
               <caption><m>R</m> is the union of two nonoverlapping regions, <m>R_1</m> and <m>R_2</m></caption>
               <!-- START figures/fig_double_region.tex -->
               <image width="35%">
@@ -1027,7 +1027,7 @@
         Evaluate the double integral <m>\iint_Rf(x,y)\, dA</m>.
       </p>
 
-      <figure xml:id="fig_double3" vshift="0">
+      <figure xml:id="fig_double3" vshift="1">
         <caption>Finding the signed volume under a surface in <xref ref="ex_double3"/></caption>
 
         <!-- START figures/figdouble3_3D.asy -->
@@ -1334,7 +1334,7 @@
         enclosing the region <m>R</m>.
       </p>
 
-      <figure xml:id="fig_double6" vshift="4">
+      <figure xml:id="fig_double6" vshift="1">
         <caption>Determining the region <m>R</m> determined by the bounds of integration in <xref ref="ex_double6"/></caption>
         <!-- START figures/fig_double6.tex -->
         <image width="47%">
@@ -2154,7 +2154,7 @@
 
         <introduction>
           <p>
-            In the following exercises:
+            For the given integral:
 
             <ol marker="(a)">
               <li>
@@ -2795,8 +2795,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            state why it is difficult/impossible to integrate the iterated integral in the given order of integration.
+            State why it is difficult/impossible to integrate the iterated integral in the given order of integration.
             Change the order of integration and evaluate the new iterated integral.
           </p>
         </introduction>
@@ -2885,8 +2884,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the average value of <m>f</m> over the region <m>R</m>.
+            Find the average value of <m>f</m> over the region <m>R</m>.
             Notice how these functions and regions are related to the iterated integrals given in
             <xref first="x13_02_ex_05" last="x13_02_ex_08" text="local">Exercises</xref>.
           </p>
diff --git a/ptx/sec_fluid_force.ptx b/ptx/sec_fluid_force.ptx
index f25fc9d98..099e8c546 100644
--- a/ptx/sec_fluid_force.ptx
+++ b/ptx/sec_fluid_force.ptx
@@ -893,7 +893,7 @@
       <exercisegroup cols="2" xml:id="exset-fluid-force-plate">
         <introduction>
           <p>
-            In the following exercises, find the fluid force exerted on the given plate,
+            Find the fluid force exerted on the given plate,
             submerged in water with a weight density of <quantity><mag>62.4</mag><unit base="pound"/><per base="foot" exp="3"/></quantity>.
           </p>
         </introduction>
@@ -1320,7 +1320,7 @@
 
       <introduction>
         <p>
-          In the following exercises, the side of a container is pictured.
+          The side of a container is pictured.
           Find the fluid force exerted on this plate when the container is full of:
         </p>
 
diff --git a/ptx/sec_graph_concavity.ptx b/ptx/sec_graph_concavity.ptx
index d90218830..3ec34877a 100644
--- a/ptx/sec_graph_concavity.ptx
+++ b/ptx/sec_graph_concavity.ptx
@@ -554,7 +554,7 @@
       shows a graph of a function with inflection points labeled.
     </p>
 
-    <figure xml:id="fig_concavity4" vshift="2">
+    <figure xml:id="fig_concavity4" vshift="0">
       <caption>A graph of a function with its inflection points marked. The intervals where concave up/down are also indicated.</caption>
       <!-- START figures/fig_concavity4.tex -->
       <image width="47%">
@@ -997,7 +997,7 @@
           shown in <xref ref="fig_conc3"/>.
         </p>
 
-        <figure xml:id="fig_conc3" vshift="2">
+        <figure xml:id="fig_conc3" vshift="-1">
           <caption>A graph of <m>S(t)</m> in <xref ref="ex_conc3"/>, modeling the sale of a product over time</caption>
           <!-- START figures/fig_conc3.tex -->
           <image width="47%">
@@ -1065,7 +1065,7 @@
           so the decline in sales is <q>leveling off.</q>
         </p>
 
-        <figure xml:id="fig_conc3b" vshift="3">
+        <figure xml:id="fig_conc3b" vshift="0">
           <caption>A graph of <m>S(t)</m> in <xref ref="ex_conc3"/>, along with <m>S'(t)</m></caption>
           <!-- START figures/fig_conc3b.tex -->
           <image width="47%">
@@ -1119,7 +1119,7 @@
       as shown in <xref ref="fig_concavity5"/>.
     </p>
 
-    <figure xml:id="fig_concavity5" vshift="-1">
+    <figure xml:id="fig_concavity5" vshift="-4">
       <caption>A graph of <m>f(x) = x^4</m>. Clearly <m>f</m> is always concave up, despite the fact that <m>\fpp(x) = 0</m> when <m>x=0</m>. In this example, the <em>possible</em> point of inflection <m>(0,0)</m> is not a point of inflection.</caption>
       <!-- START figures/fig_concavity5.tex -->
       <image width="47%">
@@ -1160,7 +1160,38 @@
       See <xref ref="fig_concavity6"/> for a visualization of this.
     </p>
 
-    <figure xml:id="fig_concavity6" vshift="-4.5">
+    <theorem xml:id="thm_second_der">
+      <title>The Second Derivative Test</title>
+      <statement>
+        <p>
+          Let <m>c</m> be a critical value of <m>f</m> where <m>\fpp(c)</m> is defined.
+          <idx><h>derivative</h><h>Second Deriv.
+          Test</h></idx>
+              <idx><h>Second Derivative Test</h></idx>
+              <idx><h>extrema</h><h>and Second Deriv. Test</h></idx>
+              <idx><h>maximum</h><h>and Second Deriv. Test</h></idx>
+              <idx><h>minimum</h><h>and First Deriv. Test</h></idx>
+
+          <ol>
+            <li>
+              <p>
+                If <m>\fpp(c)\gt 0</m>,
+                then <m>f</m> has a local minimum at <m>(c,f(c))</m>.
+              </p>
+            </li>
+
+            <li>
+              <p>
+                If <m>\fpp(c)\lt 0</m>,
+                then <m>f</m> has a local maximum at <m>(c,f(c))</m>.
+              </p>
+            </li>
+          </ol>
+        </p>
+      </statement>
+    </theorem>
+
+    <figure xml:id="fig_concavity6" vshift="1">
       <caption>Demonstrating the fact that relative maxima occur when the graph is concave down and relative minima occur when the graph is concave up</caption>
       <!-- START figures/fig_concavity6.tex -->
       <image width="47%">
@@ -1194,37 +1225,6 @@
       <!-- figures/fig_concavity6.tex END -->
     </figure>
 
-    <theorem xml:id="thm_second_der">
-      <title>The Second Derivative Test</title>
-      <statement>
-        <p>
-          Let <m>c</m> be a critical value of <m>f</m> where <m>\fpp(c)</m> is defined.
-          <idx><h>derivative</h><h>Second Deriv.
-          Test</h></idx>
-              <idx><h>Second Derivative Test</h></idx>
-              <idx><h>extrema</h><h>and Second Deriv. Test</h></idx>
-              <idx><h>maximum</h><h>and Second Deriv. Test</h></idx>
-              <idx><h>minimum</h><h>and First Deriv. Test</h></idx>
-
-          <ol>
-            <li>
-              <p>
-                If <m>\fpp(c)\gt 0</m>,
-                then <m>f</m> has a local minimum at <m>(c,f(c))</m>.
-              </p>
-            </li>
-
-            <li>
-              <p>
-                If <m>\fpp(c)\lt 0</m>,
-                then <m>f</m> has a local maximum at <m>(c,f(c))</m>.
-              </p>
-            </li>
-          </ol>
-        </p>
-      </statement>
-    </theorem>
-
     <figure xml:id="vid_graphs_concav_second_deriv_test" component="video" vshift="-4">
       <caption>Video presentation of <xref ref="thm_second_der"/></caption>
       <video youtube="4hWldEUoG2U" label="vid_graphs_concav_second_deriv_test"/>
diff --git a/ptx/sec_graph_extreme_values.ptx b/ptx/sec_graph_extreme_values.ptx
index a51bb04a8..228b3c10d 100644
--- a/ptx/sec_graph_extreme_values.ptx
+++ b/ptx/sec_graph_extreme_values.ptx
@@ -640,7 +640,7 @@
   </p>
 
   
-  <figure xml:id="fig_extreme4" vshift="1.5">
+  <figure xml:id="fig_extreme4" vshift="-1.5">
     <caption>A graph of <m>f(x)=x^3</m> which has a critical value of <m>x=0</m>, but no relative extrema</caption>
       <!-- START figures/fig_extreme4.tex -->
     <image width="47%">
@@ -1888,12 +1888,11 @@
         </exercise>
       </exercisegroup>
 
-      <enlarge-page skipsize="2"/>
-
       <exercisegroup cols="2" xml:id="exset-graph-extreme-values-find">
         <introduction>
           <p>
             Find the extreme values of the function on the given interval.
+            <enlarge-page skipsize="2"/>
           </p>
         </introduction>
         <exercise label="ex-graph-extreme-values-find-1">
diff --git a/ptx/sec_graph_incr_decr.ptx b/ptx/sec_graph_incr_decr.ptx
index d17b042c3..d11069430 100644
--- a/ptx/sec_graph_incr_decr.ptx
+++ b/ptx/sec_graph_incr_decr.ptx
@@ -991,7 +991,7 @@
         again demonstrating that <m>f</m> is increasing when <m>\fp\gt 0</m> and decreasing when <m>\fp\lt 0</m>.
       </p>
 
-      <figure xml:id="fig_incr2" vshift="2">
+      <figure xml:id="fig_incr2" vshift="1">
         <caption>A graph of <m>f(x)</m> in <xref ref="ex_incr2"/>, showing where <m>f</m> is increasing and decreasing</caption>
         <!-- START figures/fig_incr2.tex -->
         <image width="47%">
diff --git a/ptx/sec_graph_sketch.ptx b/ptx/sec_graph_sketch.ptx
index a0f905842..0bd389814 100644
--- a/ptx/sec_graph_sketch.ptx
+++ b/ptx/sec_graph_sketch.ptx
@@ -1253,8 +1253,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            practice using <xref ref="idea_sketch"/>
+            Practice using <xref ref="idea_sketch"/>
             by applying the principles to the given functions with familiar graphs.
           </p>
         </introduction>
@@ -1348,8 +1347,7 @@
   <!--TODO: Instead of "use technology", how about "use the Sage cell provided"? -->
         <introduction>
           <p>
-            In the following exercises,
-            sketch a graph of the given function using <xref ref="idea_sketch"/>.
+            Sketch a graph of the given function using <xref ref="idea_sketch"/>.
             Show all work; check your answer with technology.
           </p>
         </introduction>
@@ -1555,8 +1553,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            a function with the parameters <m>a</m> and <m>b</m> are given.
+            A function with the parameters <m>a</m> and <m>b</m> are given.
             Describe the critical points and possible points of inflection of <m>f</m> in terms of <m>a</m> and <m>b</m>.
           </p>
         </introduction>
diff --git a/ptx/sec_greensthm.ptx b/ptx/sec_greensthm.ptx
index aedf38cfd..471f62a06 100644
--- a/ptx/sec_greensthm.ptx
+++ b/ptx/sec_greensthm.ptx
@@ -1058,7 +1058,7 @@
           Find the area of <m>R</m>.
         </p>
 
-        <figure xml:id="fig_green3" vshift="0">
+        <figure xml:id="fig_green3" vshift="-1">
           <caption>The region <m>R</m>, whose area is found in <xref ref="ex_green3"/></caption>
           <image width="47%">
             <shortdescription>A teardrop-shaped region in the plane.</shortdescription>
@@ -1537,8 +1537,7 @@
       <exercisegroup cols="2" xml:id="exset-Greens-flux">
         <introduction>
           <p>
-            In the following exercises,
-            a vector field <m>\vec F</m> and a curve <m>C</m> are given.
+            A vector field <m>\vec F</m> and a curve <m>C</m> are given.
             Evaluate <m>\int_C \vec F\cdot\vec n\, ds</m>,
             the flux of <m>\vec F</m> over <m>C</m>.
           </p>
@@ -1636,8 +1635,7 @@
       <exercisegroup cols="2" xml:id="exset-Greens-verify">
         <introduction>
           <p>
-            In the following exercises,
-            a vector field <m>\vec F</m> and a closed curve <m>C</m>,
+            A vector field <m>\vec F</m> and a closed curve <m>C</m>,
             enclosing a region <m>R</m>, are given.
             Verify Green's Theorem by evaluating <m>\oint_C\vec F\cdot d\vec r</m> and
             <m>\iint_R \curl \vec F\, dA</m>, showing they are equal.
@@ -1733,8 +1731,7 @@
       <exercisegroup cols="2" xml:id="exset-Greens-area">
         <introduction>
           <p>
-            In the following exercises,
-            a closed curve <m>C</m> enclosing a region <m>R</m> is given.
+            A closed curve <m>C</m> enclosing a region <m>R</m> is given.
             Find the area of <m>R</m> by computing
             <m>\oint_C \vec F\cdot d\vec r</m> for an appropriate choice of vector field <m>\vec F</m>.
           </p>
@@ -1812,8 +1809,7 @@
       <exercisegroup cols="2" xml:id="exset-Greens-divergence">
         <introduction>
           <p>
-            In the following exercises,
-            a vector field <m>\vec F</m> and a closed curve <m>C</m>,
+            A vector field <m>\vec F</m> and a closed curve <m>C</m>,
             enclosing a region <m>R</m>, are given.
             Verify the Divergence Theorem by evaluating <m>\oint_C\vec F\cdot \vec n\, ds</m> and
             <m>\iint_R \divv \vec F\, dA</m>, showing they are equal.
diff --git a/ptx/sec_hyperbolic.ptx b/ptx/sec_hyperbolic.ptx
index f8b5ca7f9..9056df1ce 100644
--- a/ptx/sec_hyperbolic.ptx
+++ b/ptx/sec_hyperbolic.ptx
@@ -1380,8 +1380,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            verify the given identity using <xref ref="def_hyperbolic_functions"/>,
+            Verify the given identity using <xref ref="def_hyperbolic_functions"/>,
             as done in <xref ref="ex_hf1"/>.
           </p>
         </introduction>
@@ -1626,7 +1625,7 @@
 
         <introduction>
           <p>
-            In the following exercises, find the derivative of the given function.
+            Find the derivative of the given function.
           </p>
         </introduction>
   <!-- Exercise 11 -->
@@ -1875,8 +1874,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the equation of the line tangent to the function at the given <m>x</m>-value.
+            Find the equation of the line tangent to the function at the given <m>x</m>-value.
           </p>
         </introduction>
   <!-- Exercise 22 -->
@@ -2061,7 +2059,7 @@
 
         <introduction>
           <p>
-            In the following exercises, evaluate the given indefinite integral.
+            Evaluate the given indefinite integral.
           </p>
         </introduction>
   <!-- Exercise 27 -->
@@ -2362,7 +2360,7 @@
 
         <introduction>
           <p>
-            In the following exercises, evaluate the given definite integral.
+            Evaluate the given definite integral.
           </p>
         </introduction>
   <!-- Exercise 41 -->
diff --git a/ptx/sec_improper_integration.ptx b/ptx/sec_improper_integration.ptx
index d3bb81624..664dd1070 100644
--- a/ptx/sec_improper_integration.ptx
+++ b/ptx/sec_improper_integration.ptx
@@ -1490,7 +1490,7 @@
 
         <introduction>
           <p>
-            In the following exercises, evaluate the given improper integral.
+            Evaluate the given improper integral.
           </p>
         </introduction>
   <!-- Exercise 7 -->
@@ -2005,8 +2005,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            use the Direct Comparison Test or the Limit Comparison Test to determine whether the given definite integral converges or diverges.
+            Use the Direct Comparison Test or the Limit Comparison Test to determine whether the given definite integral converges or diverges.
             Clearly state what test is being used and what function the integrand is being compared to.
           </p>
         </introduction>
diff --git a/ptx/sec_int_comp_tests.ptx b/ptx/sec_int_comp_tests.ptx
index b99d22357..6e7c5b6b8 100644
--- a/ptx/sec_int_comp_tests.ptx
+++ b/ptx/sec_int_comp_tests.ptx
@@ -1001,8 +1001,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            use the Integral Test to determine the convergence of the given series.
+            Use the Integral Test to determine the convergence of the given series.
           </p>
         </introduction>
 
@@ -1147,8 +1146,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            use the Direct Comparison Test to determine the convergence of the given series;
+            Use the Direct Comparison Test to determine the convergence of the given series;
             state what series is used for comparison.
           </p>
         </introduction>
@@ -1346,8 +1344,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            use the Limit Comparison Test to determine the convergence of the given series;
+            Use the Limit Comparison Test to determine the convergence of the given series;
             state what series is used for comparison.
           </p>
         </introduction>
@@ -1529,7 +1526,7 @@
 
         <introduction>
           <p>
-            In the following exercises, determine the convergence of the given series.
+            Determine the convergence of the given series.
             State the test used; more than one test may be appropriate.
           </p>
         </introduction>
diff --git a/ptx/sec_iterated_integrals.ptx b/ptx/sec_iterated_integrals.ptx
index e1434d71f..de21e4dc3 100644
--- a/ptx/sec_iterated_integrals.ptx
+++ b/ptx/sec_iterated_integrals.ptx
@@ -555,7 +555,7 @@
           as shown in <xref ref="fig_iterated6"/>.
         </p>
 
-        <pagebreak-latex/>
+        <!-- <pagebreak-latex/> -->
 
         <figure xml:id="fig_iterated6" vshift="-2">
           <caption>Calculating the area of a plane region with iterated integrals in <xref ref="ex_iterated6"/></caption>
@@ -980,8 +980,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            evaluate the integral and subsequent iterated integral.
+            Evaluate the integral and subsequent iterated integral.
           </p>
         </introduction>
 
@@ -1190,7 +1189,7 @@
 
         <introduction>
           <p>
-            In the following exercises, a graph of a planar region <m>R</m> is given.
+            A graph of a planar region <m>R</m> is given.
             Give the iterated integrals,
             with both orders of integration <m>dy\, dx</m> and <m>dx\, dy</m>,
             that give the area of <m>R</m>.
@@ -1551,8 +1550,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            iterated integrals are given that compute the area of a region <m>R</m> in the <m>xy</m>-plane.
+            Iterated integrals are given that compute the area of a region <m>R</m> in the <m>xy</m>-plane.
             Sketch the region <m>R</m>,
             and give the iterated integral(s) that give the area of <m>R</m> with the opposite order of integration.
           </p>
diff --git a/ptx/sec_limit_analytically.ptx b/ptx/sec_limit_analytically.ptx
index c15f59659..03d67c50a 100644
--- a/ptx/sec_limit_analytically.ptx
+++ b/ptx/sec_limit_analytically.ptx
@@ -667,7 +667,7 @@
         Later we will show that we can also consider <m>\theta \leq 0</m>.)
       </p>
 
-      <figure xml:id="fig_squeeze_sinx" vshift="-5.75">
+      <figure xml:id="fig_squeeze_sinx" vshift="-2">
         <caption>The unit circle and related triangles</caption>
         <!-- START figures/fig_squeeze1.tex -->
         <image width="47%">
diff --git a/ptx/sec_limit_continuity.ptx b/ptx/sec_limit_continuity.ptx
index d0bcf4eee..15d835226 100644
--- a/ptx/sec_limit_continuity.ptx
+++ b/ptx/sec_limit_continuity.ptx
@@ -805,7 +805,7 @@
         and <xref ref="thm_continuous_functions" text="global"/> as appropriate.
       </p>
 
-      <figure xml:id="fig_continuous3" vshift="0">
+      <figure xml:id="fig_continuous3" vshift="0.5">
         <caption>A graph of <m>f(x)=\sqrt{x-1}+\sqrt{5-x}</m></caption>
         <!-- START figures/fig_continuous3.tex -->
         <image width="47%">
diff --git a/ptx/sec_limit_intro.ptx b/ptx/sec_limit_intro.ptx
index 6be1db13a..7e5b10c66 100644
--- a/ptx/sec_limit_intro.ptx
+++ b/ptx/sec_limit_intro.ptx
@@ -897,10 +897,7 @@
 
         <p>
           Since <m>f(x)</m> is not approaching a single number, we conclude that
-          <md>
-            \lim_{x\to 1}\frac{1}{(x-1)^2}
-          </md>
-          does not exist.
+          <m>\lim_{x\to 1}\frac{1}{(x-1)^2}</m> does not exist.
         </p>
       </solution>
     </example>
@@ -1245,7 +1242,7 @@
       See <xref ref="fig_diffquot1"/>.
     </p>
 
-    <figure xml:id="fig_diffquot1" vshift="3">
+    <figure xml:id="fig_diffquot1" vshift="2">
       <caption>Interpreting a difference quotient as the slope of a secant line</caption>
       <!-- START figures/fig_diff_quot1.tex -->
       <image width="47%">
diff --git a/ptx/sec_line_int_intro.ptx b/ptx/sec_line_int_intro.ptx
index b9a3fadd2..010d01f6b 100644
--- a/ptx/sec_line_int_intro.ptx
+++ b/ptx/sec_line_int_intro.ptx
@@ -1506,8 +1506,7 @@
       <exercisegroup cols="2" xml:id="exset-line-int-intro-scalar-function">
         <introduction>
           <p>
-            In the following exercises,
-            a planar curve <m>C</m> is given along with a function <m>f</m> that is defined over <m>C</m>.
+            A planar curve <m>C</m> is given along with a function <m>f</m> that is defined over <m>C</m>.
             Evaluate the line integral <m>\ds \int_Cf(s)\, ds</m>.
           </p>
         </introduction>
@@ -1609,8 +1608,7 @@
       <exercisegroup cols="2" xml:id="exset-line-int-scalar-technology">
         <introduction>
           <p>
-            In the following exercises,
-            a planar curve <m>C</m> is given along with a function <m>f</m> that is defined over <m>C</m>.
+            A planar curve <m>C</m> is given along with a function <m>f</m> that is defined over <m>C</m>.
             Set up the line integral <m>\ds \int_Cf(s)\, ds</m>,
             then approximate its value using technology.
           </p>
@@ -1676,7 +1674,7 @@
       <exercisegroup cols="2" xml:id="exset-line-int-intro-area">
         <introduction>
           <p>
-            In the following exercises, a parametrized curve <m>C</m> in space is given.
+            A parametrized curve <m>C</m> in space is given.
             Find the area above the <m>xy</m>-plane that is under <m>C</m>.
           </p>
         </introduction>
@@ -1738,8 +1736,7 @@
       <exercisegroup cols="2" xml:id="exset-line-int-intro-mass">
         <introduction>
           <p>
-            In the following exercises,
-            a parametrized curve <m>C</m> is given that represents a thin wire with density <m>\delta</m>.
+            A parametrized curve <m>C</m> is given that represents a thin wire with density <m>\delta</m>.
             Find the mass and center of mass of the thin wire.
           </p>
         </introduction>
diff --git a/ptx/sec_line_int_vf.ptx b/ptx/sec_line_int_vf.ptx
index 2b3015a07..be19afe22 100644
--- a/ptx/sec_line_int_vf.ptx
+++ b/ptx/sec_line_int_vf.ptx
@@ -1616,8 +1616,7 @@
       <exercisegroup cols="2" xml:id="exset-line-int-vector-evaluate">
         <introduction>
           <p>
-            In the following exercises,
-            a vector field <m>\vec F</m> and a curve <m>C</m> are given.
+            A vector field <m>\vec F</m> and a curve <m>C</m> are given.
             Evaluate <m>\ds\int_C\vec F\cdot d\vec r</m>.
           </p>
         </introduction>
@@ -1716,8 +1715,7 @@
       <exercisegroup cols="2" xml:id="exset-line-int-vector-work">
         <introduction>
           <p>
-            In the following exercises,
-            find the work performed by the force field <m>\vec F</m> moving a particle along the path <m>C</m>.
+            Find the work performed by the force field <m>\vec F</m> moving a particle along the path <m>C</m>.
           </p>
         </introduction>
 
@@ -1788,9 +1786,8 @@
       <exercisegroup cols="2" xml:id="exset-line-int-vector-conservative">
         <introduction>
           <p>
-            In the following exercises,
-            a conservative vector field <m>\vec F</m> and a curve <m>C</m> are given.
-
+            A conservative vector field <m>\vec F</m> and a curve <m>C</m> are given.
+            <enlarge-page skipsize="2"/>
             <ol>
               <li>
                 <p>
diff --git a/ptx/sec_lines.ptx b/ptx/sec_lines.ptx
index 85a79a0e3..5f11d533a 100644
--- a/ptx/sec_lines.ptx
+++ b/ptx/sec_lines.ptx
@@ -594,9 +594,21 @@
           (where the points and directions indicated by the equations of each line are identified).
         </p>
 
-        <pagebreak-latex component="novideo"/>
+        <!-- <pagebreak-latex component="novideo"/> -->
         
-        <figure xml:id="fig_lines2" vshift="-3">
+        <p>
+          We next check to see if they intersect
+          (if they do not, they are skew lines).
+          To find if they intersect,
+          we look for <m>t</m> and <m>s</m> values such that the respective <m>x</m>,
+          <m>y</m> and <m>z</m> values are the same.
+          That is, we want <m>s</m> and <m>t</m> such that:
+          <md>
+            \begin{matrix} 1+3t \amp =\amp -2+4s\\ 2-t\amp =\amp 3+s\\ t\amp =\amp 5+2s \end{matrix}
+          </md>.
+        </p>
+
+        <figure xml:id="fig_lines2" vshift="0">
           <caption>Sketching the lines from <xref ref="ex_lines2"/></caption>
 
           <!-- START figures/figlines2_3D.asy -->
@@ -671,18 +683,6 @@
           <!-- figures/figlines2_3D.asy END -->
         </figure>
 
-        <p>
-          We next check to see if they intersect
-          (if they do not, they are skew lines).
-          To find if they intersect,
-          we look for <m>t</m> and <m>s</m> values such that the respective <m>x</m>,
-          <m>y</m> and <m>z</m> values are the same.
-          That is, we want <m>s</m> and <m>t</m> such that:
-          <md>
-            \begin{matrix} 1+3t \amp =\amp -2+4s\\ 2-t\amp =\amp 3+s\\ t\amp =\amp 5+2s \end{matrix}
-          </md>.
-        </p>
-
         <p>
           This is a relatively simple system of linear equations.
           Since the last equation is already solved for <m>t</m>,
@@ -891,7 +891,7 @@
       will help establish a general method of computing this distance <m>h</m>.
     </p>
 
-    <figure xml:id="fig_lines_dist1" vshift="3">
+    <figure xml:id="fig_lines_dist1" vshift="1">
       <caption>Establishing the distance from a point to a line</caption>
       <!-- START figures/fig_lines_dist1.tex -->
       <image width="47%">
diff --git a/ptx/sec_multi_chain.ptx b/ptx/sec_multi_chain.ptx
index ad854ac95..be39acc87 100644
--- a/ptx/sec_multi_chain.ptx
+++ b/ptx/sec_multi_chain.ptx
@@ -1180,8 +1180,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            functions <m>z=f(x,y)</m>, <m>x=g(t)</m> and <m>y=h(t)</m> are given.
+            Functions <m>z=f(x,y)</m>, <m>x=g(t)</m> and <m>y=h(t)</m> are given.
             Find the values of <m>t</m> where <m>\frac{dz}{dt}=0</m>.
             Note: these are the same surfaces/curves as found in <xref first="x12_08_ex_07" last="x12_08_ex_08" text="local">Exercises</xref>.
           </p>
diff --git a/ptx/sec_multi_extreme_values.ptx b/ptx/sec_multi_extreme_values.ptx
index 31ca2db3c..332757b63 100644
--- a/ptx/sec_multi_extreme_values.ptx
+++ b/ptx/sec_multi_extreme_values.ptx
@@ -357,7 +357,7 @@
           we consider the graph of <m>f</m> in <xref ref="fig_multi_extreme3"/>.
         </p>
 
-        <figure xml:id="fig_multi_extreme3" vshift="1">
+        <figure xml:id="fig_multi_extreme3" vshift="-1">
           <caption>The surface in <xref ref="ex_multi_extreme3"/> with both critical points marked</caption>
 
           <!-- START figures/figmulti_extreme3_3D.asy -->
@@ -1881,7 +1881,7 @@
                   The absolute maximum happens for input:
                 </instruction>
                 <p>
-                  <var name="$maxin" width="10"/>.
+                  <var name="$maxin" width="10"/>
                 </p>
 
                 <instruction>
@@ -1895,7 +1895,7 @@
                  The absolute minimum happens for input:
                 </instruction>
                 <p>
-                   <var name="$minin" width="10"/>.
+                   <var name="$minin" width="10"/>
                 </p>
               </statement>
               <solution>
@@ -1956,7 +1956,7 @@
                   The absolute maximum happens for input:
                 </instruction>
                 <p>
-                  <var name="$maxin" width="10"/>.
+                  <var name="$maxin" width="10"/>
                 </p>
 
                 <instruction>
@@ -1970,7 +1970,7 @@
                  The absolute minimum happens for input:
                 </instruction>
                 <p>
-                   <var name="$minin" width="10"/>.
+                   <var name="$minin" width="10"/>
                 </p>
               </statement>
               <solution>
diff --git a/ptx/sec_multi_intro.ptx b/ptx/sec_multi_intro.ptx
index 7bbc1fac5..5f64ca6f9 100644
--- a/ptx/sec_multi_intro.ptx
+++ b/ptx/sec_multi_intro.ptx
@@ -101,7 +101,7 @@
           we can write <m>D = \{(x,y)|\,\frac{x^2}9+\frac{y^2}4 \leq 1\}</m>.
         </p>
 
-        <figure xml:id="fig_multi2" vshift="-2">
+        <figure xml:id="fig_multi2" vshift="0">
           <caption>Illustrating the domain of <m>f(x,y)</m> in <xref ref="ex_multi2"/></caption>
           <!-- START figures/fig_multi2.tex -->
           <image width="47%">
@@ -1079,8 +1079,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            give the domain and range of the multivariable function.
+            Give the domain and range of the multivariable function.
           </p>
         </introduction>
 
@@ -1262,8 +1261,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            describe in words and sketch the level curves for the function and given <m>c</m> values.
+            Describe in words and sketch the level curves for the function and given <m>c</m> values.
           </p>
         </introduction>
 
@@ -1426,8 +1424,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            give the domain and range of the functions of three variables.
+            Give the domain and range of the functions of three variables.
           </p>
         </introduction>
 
@@ -1525,8 +1522,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            describe the level surfaces of the given functions of three variables.
+            Describe the level surfaces of the given functions of three variables.
           </p>
         </introduction>
 
diff --git a/ptx/sec_multi_limit.ptx b/ptx/sec_multi_limit.ptx
index 686683a91..edd11bb8d 100644
--- a/ptx/sec_multi_limit.ptx
+++ b/ptx/sec_multi_limit.ptx
@@ -1515,14 +1515,14 @@
 
         <introduction>
           <p>
-            In the following exercises:
+            For the given function:
           </p>
 
           <p>
             <ol marker="(a)">
               <li>
                 <p>
-                  Find the domain <m>D</m> of the given function.
+                  Find the domain <m>D</m> of the function.
                 </p>
               </li>
 
@@ -1686,7 +1686,7 @@
 
         <introduction>
           <p>
-            In the following exercises, a limit is given.
+            A limit is given.
             Evaluate the limit along the paths given,
             then state why these results show the given limit does not exist.
           </p>
diff --git a/ptx/sec_newton.ptx b/ptx/sec_newton.ptx
index b4214eb97..f65f84dd9 100644
--- a/ptx/sec_newton.ptx
+++ b/ptx/sec_newton.ptx
@@ -571,7 +571,9 @@
     in this case, <c>0.0000000001</c>.
   </p>
 
-  <paragraphs>
+  <!-- <pagebreak-latex/> -->
+  
+  <paragraphs xml:id="paragraphs-newton-convergence">
     <title>Convergence of Newton's Method</title>
     <p>
       What should one use for the initial guess, <m>x_0</m>?
diff --git a/ptx/sec_numerical_integration.ptx b/ptx/sec_numerical_integration.ptx
index 880b7448e..2c9a824b3 100644
--- a/ptx/sec_numerical_integration.ptx
+++ b/ptx/sec_numerical_integration.ptx
@@ -2209,8 +2209,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            approximate the definite integral with the Trapezoidal Rule and Simpson's Rule,
+            Approximate the definite integral with the Trapezoidal Rule and Simpson's Rule,
             with <m>n=4</m>. Then find the exact value.
           </p>
         </introduction>
@@ -2812,8 +2811,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            approximate the definite integral with the Trapezoidal Rule and Simpson's Rule,
+            Approximate the definite integral with the Trapezoidal Rule and Simpson's Rule,
             with <m>n=6</m>.
           </p>
         </introduction>
@@ -3303,8 +3301,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find <m>n</m> such that the error in approximating the given definite integral is less than <m>0.0001</m>
+            Find <m>n</m> such that the error in approximating the given definite integral is less than <m>0.0001</m>
             when using the Trapezoidal Rule and Simpson's Rule.
           </p>
         </introduction>
@@ -3520,7 +3517,7 @@
 
         <introduction>
           <p>
-            In the following exercises, a region is given.
+            A region is given.
             Find the area of the region using Simpson's Rule:
           </p>
 
diff --git a/ptx/sec_par_calc.ptx b/ptx/sec_par_calc.ptx
index 295d16c6e..e080451ee 100644
--- a/ptx/sec_par_calc.ptx
+++ b/ptx/sec_par_calc.ptx
@@ -1053,7 +1053,7 @@
           <m>y=t^2-1</m> crosses itself as shown in <xref ref="fig_parcalc7"/>,
           forming a <q>teardrop.</q> Find the arc length of the teardrop.
         </p>
-        <figure xml:id="fig_parcalc7" vshift="2">
+        <figure xml:id="fig_parcalc7" vshift="-2">
           <caption>A graph of the parametric equations in <xref ref="ex_parcalc7"/>, where the arc length of the teardrop is calculated</caption>
           <!-- START figures/fig_parcalc7.tex -->
           <image width="47%">
@@ -1280,7 +1280,7 @@
           Find the surface area if this shape is rotated about the <m>x</m>-axis,
           as shown in <xref ref="fig_parcalc8"/>.
         </p>
-        <figure xml:id="fig_parcalc8" vshift="0">
+        <figure xml:id="fig_parcalc8" vshift="-1">
           <caption>Rotating a teardrop shape about the <m>x</m>-axis in <xref ref="ex_parcalc8"/></caption>
 
           <!-- START figures/figparcalc8_3D.asy -->
@@ -1475,7 +1475,7 @@
 
         <introduction>
           <p>
-            In the following exercises, parametric equations for a curve are given.
+            Parametric equations for a curve are given.
           </p>
 
           <p>
@@ -2362,7 +2362,7 @@
 
         <introduction>
           <p>
-            In the following exercises, numerically approximate the given arc length.
+            Numerically approximate the given arc length.
           </p>
         </introduction>
 
@@ -2445,7 +2445,7 @@
 
         <introduction>
           <p>
-            In the following exercises, a solid of revolution is described.
+            A solid of revolution is described.
             Find or approximate its surface area as specified.
           </p>
         </introduction>
diff --git a/ptx/sec_param_eqs.ptx b/ptx/sec_param_eqs.ptx
index bd91e4c0a..a4f211604 100644
--- a/ptx/sec_param_eqs.ptx
+++ b/ptx/sec_param_eqs.ptx
@@ -887,7 +887,7 @@
           as shown in <xref ref="fig_pareq6"/>.
         </p>
 
-        <figure xml:id="fig_pareq6" vshift="0">
+        <figure xml:id="fig_pareq6" vshift="3">
           <caption>Graphing projectile motion in <xref ref="ex_pareq6"/></caption>
           <!-- START figures/fig_pareq6.tex -->
           <image width="47%">
@@ -1072,7 +1072,7 @@
           </md>
         </p>
 
-        <figure xml:id="fig_pareq8" vshift="-5">
+        <figure xml:id="fig_pareq8" vshift="0">
           <caption>Graphing the parametric equations <m>x=4\cos(t) +3</m>, <m>y=2\sin(t) +1</m> in <xref ref="ex_pareq8"/></caption>
           <!-- START figures/fig_pareq8.tex -->
           <image width="47%">
@@ -1538,7 +1538,7 @@
           illustrating the cusp at <m>(1,4)</m>.
         </p>
 
-        <figure xml:id="fig_pareq9" vshift="-3">
+        <figure xml:id="fig_pareq9" vshift="0">
           <caption>Graphing the curve in <xref ref="ex_pareq9"/>; note it is not smooth at <m>(1,4)</m></caption>
           <!-- START figures/fig_pareq9.tex -->
           <image width="47%">
@@ -1717,8 +1717,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            sketch the graph of the given parametric equations <em>by hand</em>,
+            Sketch the graph of the given parametric equations <em>by hand</em>,
             making a table of points to plot.
             Be sure to indicate the orientation of the graph.
           </p>
@@ -1915,8 +1914,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            sketch the graph of the given parametric equations;
+            Sketch the graph of the given parametric equations;
             using a graphing utility is advisable.
             Be sure to indicate the orientation of the graph.
           </p>
@@ -2358,7 +2356,7 @@
 
         <introduction>
           <p>
-            In the following exercises, four sets of parametric equations are given.
+            Four sets of parametric equations are given.
             Describe how their graphs are similar and different.
             Be sure to discuss orientation and ranges.
           </p>
@@ -2676,8 +2674,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            eliminate the parameter in the given parametric equations.
+            Eliminate the parameter in the given parametric equations.
             Describe the curve defined by the parametric equations based on its rectangular form.
           </p>
         </introduction>
@@ -2762,8 +2759,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find parametric equations for the given rectangular equation using the parameter <m>\ds t=\frac{dy}{dx}</m>.
+            Find parametric equations for the given rectangular equation using the parameter <m>\ds t=\frac{dy}{dx}</m>.
             Verify that at <m>t=1</m>,
             the point on the graph has a tangent line with slope of 1.
           </p>
@@ -2978,8 +2974,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the values of <m>t</m> where the graph of the parametric equations crosses itself.
+            Find the values of <m>t</m> where the graph of the parametric equations crosses itself.
           </p>
         </introduction>
 
@@ -3073,8 +3068,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the value(s) of <m>t</m> where the curve defined by the parametric equations is not smooth.
+            Find the value(s) of <m>t</m> where the curve defined by the parametric equations is not smooth.
           </p>
         </introduction>
 
diff --git a/ptx/sec_parametric_surfaces.ptx b/ptx/sec_parametric_surfaces.ptx
index 1fab7597c..ca249a81f 100644
--- a/ptx/sec_parametric_surfaces.ptx
+++ b/ptx/sec_parametric_surfaces.ptx
@@ -894,7 +894,7 @@
           where <m>-1\leq y\leq 2</m>,
           as shown in <xref ref="fig_parsurf5"/>.
         </p>
-        <figure xml:id="fig_parsurf5" vshift="0">
+        <figure xml:id="fig_parsurf5" vshift="-1">
           <caption>The cylinder parametrized in <xref ref="ex_parsurf5"/></caption>
           <image width="47%">
             <shortdescription>A cylindrical surface centered along the y axis.</shortdescription>
@@ -992,7 +992,7 @@
           where <m>-2\leq z\leq 3</m>,
           as shown in <xref ref="fig_parsurf6a"/>.
         </p>
-        <figure xml:id="fig_parsurf6a" vshift="0">
+        <figure xml:id="fig_parsurf6a" vshift="-1">
           <caption>The elliptic cone as described in  <xref ref="ex_parsurf6"/></caption>
           <image width="47%">
             <shortdescription>An elliptic cone with its cusp at the origin, including portions above and below the x,y plane.</shortdescription>
@@ -1874,8 +1874,7 @@
       <exercisegroup cols="2" xml:id="exset-parametrize-surface">
         <introduction>
           <p>
-            In the following exercises,
-            parametrize the surface defined by the function
+            Parametrize the surface defined by the function
             <m>z=f(x,y)</m> over each of the given regions <m>R</m> of the <m>xy</m>-plane.
           </p>
         </introduction>
@@ -2024,8 +2023,7 @@
       <exercisegroup cols="2">
         <introduction>
           <p>
-            In the following exercises,
-            a surface <m>\surfaceS</m> in space is described that cannot be defined as the graph of a function <m>f(x,y)</m>.
+            A surface <m>\surfaceS</m> in space is described that cannot be defined as the graph of a function <m>f(x,y)</m>.
             Give a parametrization of <m>\surfaceS</m>.
           </p>
         </introduction>
@@ -2095,7 +2093,7 @@
     <exercisegroup cols="2" xml:id="exset-parametrize-boundary">
       <introduction>
         <p>
-          In the following exercises, a domain <m>D</m> in space is given.
+          A domain <m>D</m> in space is given.
           Parametrize each of the bounding surfaces of <m>D</m>.
         </p>
       </introduction>
@@ -3118,8 +3116,7 @@
       <exercisegroup cols="2" xml:id="exset-parametric-surface-area-exact">
         <introduction>
           <p>
-            In the following exercises,
-            find the surface area <m>S</m> of the given surface <m>\surfaceS</m>. (The associated integrals are computable without the assistance of technology.)
+            Find the surface area <m>S</m> of the given surface <m>\surfaceS</m>. (The associated integrals are computable without the assistance of technology.)
           </p>
         </introduction>
 
@@ -3184,8 +3181,7 @@
       <exercisegroup cols="2" xml:id="exset-parametric-surface-area-approx">
         <introduction>
           <p>
-            In the following exercises,
-            set up the double integral that finds the surface area <m>S</m> of the given surface <m>\surfaceS</m>, then use technology to approximate its value.
+            Set up the double integral that finds the surface area <m>S</m> of the given surface <m>\surfaceS</m>, then use technology to approximate its value.
           </p>
         </introduction>
 
diff --git a/ptx/sec_partial_derivatives.ptx b/ptx/sec_partial_derivatives.ptx
index e07b6357b..20dc233d5 100644
--- a/ptx/sec_partial_derivatives.ptx
+++ b/ptx/sec_partial_derivatives.ptx
@@ -761,7 +761,7 @@
       Now that we understand functions of multiple variables,
       we see the importance of specifying which variables we are referring to.
     </p>
-    <aside vshift="0">
+    <aside vshift="2">
       <p>
         The terms in <xref ref="def_second_partial"/> all depend on limits,
         so each definition comes with the caveat
@@ -1526,8 +1526,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            evaluate <m>f_x(x,y)</m> and
+            Evaluate <m>f_x(x,y)</m> and
             <m>f_y(x,y)</m> at the indicated point.
           </p>
         </introduction>
@@ -1640,7 +1639,7 @@
 
         <introduction>
           <p>
-            In the following exercises, find <m>f_x</m>, <m>f_y</m>,
+            Find <m>f_x</m>, <m>f_y</m>,
             <m>f_{xx}</m>, <m>f_{yy}</m>,
             <m>f_{xy}</m> and <m>f_{yx}</m>.
           </p>
@@ -2447,8 +2446,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            form a function <m>f(x,y)</m> such that <m>f_x</m> and <m>f_y</m> match those given.
+            Form a function <m>f(x,y)</m> such that <m>f_x</m> and <m>f_y</m> match those given.
           </p>
         </introduction>
 
@@ -2533,7 +2531,7 @@
 
         <introduction>
           <p>
-            In the following exercises, find <m>f_x</m>,
+            Find <m>f_x</m>,
             <m>f_y</m>, <m>f_z</m>, <m>f_{yz}</m> and <m>f_{zy}</m>.
           </p>
         </introduction>
diff --git a/ptx/sec_planes.ptx b/ptx/sec_planes.ptx
index f4a94a90b..a7d1e2a54 100644
--- a/ptx/sec_planes.ptx
+++ b/ptx/sec_planes.ptx
@@ -207,7 +207,7 @@
           The plane is sketched in <xref ref="fig_planes1"/>.
         </p>
 
-        <figure xml:id="fig_planes1" vshift="-5">
+        <figure xml:id="fig_planes1" vshift="0">
           <caption>Sketching the plane in <xref ref="ex_planes1"/></caption>
 
           <!-- START figures/figplanes1_3D.asy -->
@@ -465,7 +465,7 @@
           The line and plane are sketched in <xref ref="fig_planes3"/>.
         </p>
 
-        <figure xml:id="fig_planes3" vshift="-4">
+        <figure xml:id="fig_planes3" vshift="-1">
           <caption>The line and plane in <xref ref="ex_planes3"/></caption>
 
           <!-- START figures/figplanes3_3D.asy -->
@@ -605,7 +605,7 @@
           The planes and line are graphed in <xref ref="fig_planes4"/>.
         </p>
 
-        <figure xml:id="fig_planes4" vshift="-2">
+        <figure xml:id="fig_planes4" vshift="0">
           <caption>Graphing the planes and their line of intersection in <xref ref="ex_planes4"/></caption>
 
           <!-- START figures/figplanes4_3D.asy -->
@@ -732,7 +732,7 @@
           illustrated in <xref ref="fig_planes5"/>.
         </p>
 
-        <figure xml:id="fig_planes5" vshift="-2.5">
+        <figure xml:id="fig_planes5" vshift="0">
           <caption>Illustrating the intersection of a line and a plane in <xref ref="ex_planes5"/></caption>
 
           <!-- START figures/figplanes5_3D.asy -->
@@ -1036,7 +1036,7 @@
 
         <introduction>
           <p>
-            In the following exercises, give any two points in the given plane.
+            Give any two points in the given plane.
           </p>
         </introduction>
 
@@ -1183,8 +1183,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            give the equation of the described plane in standard and general forms.
+            Give the equation of the described plane in standard and general forms.
           </p>
         </introduction>
 
@@ -1935,8 +1934,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            give the equation of the line that is the intersection of the given planes.
+            Give the equation of the line that is the intersection of the given planes.
           </p>
         </introduction>
 
diff --git a/ptx/sec_polar.ptx b/ptx/sec_polar.ptx
index 3106688ac..affb0ac54 100644
--- a/ptx/sec_polar.ptx
+++ b/ptx/sec_polar.ptx
@@ -528,7 +528,7 @@
     </example>
   </subsection>
 
-  <subsection>
+  <subsection xml:id="subsec-polar-graphs">
     <title>Polar Functions and Polar Graphs</title>
     <p>
       Defining a new coordinate system allows us to create a new kind of function,
@@ -814,7 +814,7 @@
       in <xref ref="fig_polar4c"/>.
     </p>
 
-    <figure xml:id="fig_polar4c" vshift="5">
+    <figure xml:id="fig_polar4c" vshift="6">
       <caption>Using  technology to graph a polar function</caption>
       <!-- START figures/fig_polar4c.tex -->
       <image width="47%">
@@ -874,7 +874,7 @@
           we numbered each point in the table and on the graph.
         </p>
 
-        <figure xml:id="fig_polar5table" vshift="0">
+        <figure xml:id="fig_polar5table" vshift="1">
           <caption>Table of points for plotting a polar curve in <xref ref="ex_polar5"/></caption>
           <tabular halign="center">
             <row bottom="minor"><cell>Pt.</cell><cell><m>\theta</m></cell><cell><m>\cos(2\theta)</m></cell></row>
@@ -1626,7 +1626,7 @@
         Symmetric about <m>y</m>-axis: <m>r=a\pm b\sin(\theta)</m>; <m>a,b \gt 0</m>
       </p>
 
-      <pagebreak-latex/>
+      <!-- <pagebreak-latex/> -->
       
       <figure xml:id="fig_polar_roses" hstretch="450">
         <caption>Rose curves</caption>
@@ -2650,7 +2650,7 @@
 
           <introduction>
             <p>
-              In the following exercises, graph the polar function on the given interval.
+              Graph the polar function on the given interval.
             </p>
           </introduction>
 
@@ -3505,8 +3505,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            convert the polar equation to a rectangular equation.
+            Convert the polar equation to a rectangular equation.
           </p>
         </introduction>
 
@@ -3721,8 +3720,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            convert the rectangular equation to a polar equation.
+            Convert the rectangular equation to a polar equation.
           </p>
         </introduction>
 
@@ -3910,8 +3908,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the points of intersection of the polar graphs.
+            Find the points of intersection of the polar graphs.
           </p>
         </introduction>
 
diff --git a/ptx/sec_polarcalc.ptx b/ptx/sec_polarcalc.ptx
index ad85416ff..f90576c71 100644
--- a/ptx/sec_polarcalc.ptx
+++ b/ptx/sec_polarcalc.ptx
@@ -288,7 +288,7 @@
           we zoom in on the tangent lines in <xref ref="fig_polcalc2"/>.
         </p>
 
-        <figure xml:id="fig_polcalc2" vshift="-1">
+        <figure xml:id="fig_polcalc2" vshift="2">
           <caption>Graphing the tangent lines at the pole in <xref ref="ex_polcalc2"/></caption>
           <!-- START figures/fig_polcalc2.tex -->
           <image width="47%">
@@ -607,7 +607,7 @@
       </solution>
     </example>
 
-    <aside vshift="8">
+    <aside vshift="5">
       <p>
         <xref ref="ex_polcalc3"/>
         requires the use of the integral <m>\ds\int \cos^2(\theta) \,d\theta</m>.
@@ -634,7 +634,7 @@
           as shown in <xref ref="fig_polcalc4"/>.
         </p>
 
-        <figure xml:id="fig_polcalc4" vshift="0.5">
+        <figure xml:id="fig_polcalc4" vshift="-1">
           <caption>Finding the area of the shaded region of a cardioid in <xref ref="ex_polcalc4"/></caption>
           <!-- START figures/fig_polcalc4.tex -->
           <image width="47%">
@@ -1122,7 +1122,7 @@
           </md>.
         </p>
 
-        <figure xml:id="fig_polcalc7" vshift="-4">
+        <figure xml:id="fig_polcalc7" vshift="0">
           <caption>The limaçon in <xref ref="ex_polcalc7"/> whose arc length is measured</caption>
           <!-- START figures/fig_polcalc7.tex -->
           <image width="47%">
@@ -2275,7 +2275,7 @@
 
         <introduction>
           <p>
-            In the following exercises, answer the questions involving arc length.
+            Answer the questions involving arc length.
           </p>
         </introduction>
 
@@ -2410,7 +2410,7 @@
 
         <introduction>
           <p>
-            In the following exercises, answer the questions involving surface area.
+            Answer the questions involving surface area.
           </p>
         </introduction>
 
diff --git a/ptx/sec_power_series.ptx b/ptx/sec_power_series.ptx
index 1625874a7..644192cf0 100644
--- a/ptx/sec_power_series.ptx
+++ b/ptx/sec_power_series.ptx
@@ -1028,8 +1028,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            write out the sum of the first 5 terms of the given power series.
+            Write out the sum of the first 5 terms of the given power series.
           </p>
         </introduction>
 
@@ -1106,7 +1105,7 @@
 
         <introduction>
           <p>
-            In the following exercises, a power series is given.
+            A power series is given.
           </p>
 
           <p>
@@ -1595,8 +1594,7 @@
 
       <introduction>
         <p>
-          In the following exercises,
-          a function <m>\ds f(x) = \infser[0] a_nx^n</m> is given.
+          A function <m>\ds f(x) = \infser[0] a_nx^n</m> is given.
         </p>
 
         <p>
@@ -1803,8 +1801,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            give the first 5 terms of the series that is a solution to the given differential equation.
+            Give the first 5 terms of the series that is a solution to the given differential equation.
           </p>
         </introduction>
 
diff --git a/ptx/sec_ratio_root_tests.ptx b/ptx/sec_ratio_root_tests.ptx
index 1ae8f6673..449d031f3 100644
--- a/ptx/sec_ratio_root_tests.ptx
+++ b/ptx/sec_ratio_root_tests.ptx
@@ -618,8 +618,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            determine the convergence of the given series using the Ratio Test.
+            Determine the convergence of the given series using the Ratio Test.
             If the Ratio Test is inconclusive,
             state so and determine convergence with another test.
           </p>
@@ -804,8 +803,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            determine the convergence of the given series using the Root Test.
+            Determine the convergence of the given series using the Root Test.
             If the Root Test is inconclusive,
             state so and determine convergence with another test.
           </p>
@@ -990,7 +988,7 @@
 
         <introduction>
           <p>
-            In the following exercises, determine the convergence of the given series.
+            Determine the convergence of the given series.
             State the test used; more than one test may be appropriate.
           </p>
         </introduction>
diff --git a/ptx/sec_riemann.ptx b/ptx/sec_riemann.ptx
index f73d7bb1b..c65ccce77 100644
--- a/ptx/sec_riemann.ptx
+++ b/ptx/sec_riemann.ptx
@@ -1488,7 +1488,7 @@
           Using <m>n=100</m> gives an approximation of <m>159.802</m>.
         </p>
 
-        <figure xml:id="fig_rie9" vshift="1">
+        <figure xml:id="fig_rie9" vshift="0.5">
           <caption>Approximating <m>\int_{-1}^5 x^3\, dx</m> using the Right Hand Rule and 10 evenly spaced subintervals</caption>
           <!-- START figures/fig_rie9.tex -->
           <image width="47%">
@@ -1693,7 +1693,7 @@
     </aside>
 
 
-    <p>
+    <p xml:id="riemann-summary-break">
       We summarize what we have learned over the past few sections here.
     </p>
 
@@ -2735,7 +2735,7 @@
       <exercisegroup cols="2" xml:id="exset-riemann-integral-approx">
         <introduction>
           <p>
-            In the following exercises, a definite integral <m>\ds \int_a^b f(x) \, dx</m> is given.
+            A definite integral <m>\ds \int_a^b f(x) \, dx</m> is given.
             <ol>
               <li>
                 <p>
diff --git a/ptx/sec_sequences.ptx b/ptx/sec_sequences.ptx
index b20b8e088..7198944ad 100644
--- a/ptx/sec_sequences.ptx
+++ b/ptx/sec_sequences.ptx
@@ -153,8 +153,8 @@
               and the values of the terms are plotted on the vertical axis.
               To visualize this sequence, see <xref ref="fig_seq1a"/>.
             </p>
-            <figure xml:id="fig_seq1a" vshift="5">
-              <caption>Plotting the sequence in <xref ref="item_ex_seq1_1"/></caption>
+            <figure xml:id="fig_seq1a" vshift="6">
+              <caption>Plotting the sequence in <xref ref="item_ex_seq1_1"/> of <xref ref="ex_seq1"/></caption>
         <!-- START figures/fig_seq1a.tex -->
               <image width="47%">
                 <shortdescription>Plot of the first four terms of the sequence in part 1 of this example.</shortdescription>
@@ -205,8 +205,8 @@
               consisting of only the values 3 and 5.
               This sequence is plotted in <xref ref="fig_seq1b"/>.
             </p>
-            <figure xml:id="fig_seq1b" vshift="0">
-              <caption>Plotting the sequence in <xref ref="item_ex_seq1_2"/></caption>
+            <figure xml:id="fig_seq1b" vshift="1.25">
+              <caption>Plotting the sequence in <xref ref="item_ex_seq1_2"/> of <xref ref="ex_seq1"/></caption>
         <!-- START figures/fig_seq1b.tex -->
               <image width="47%">
                 <shortdescription>A plot of the first four terms of the sequence in part 2 of this example.</shortdescription>
@@ -262,8 +262,8 @@
               due to the fact that the exponent of <m>-1</m> is a special quadratic.
               This sequence is plotted in <xref ref="fig_seq1c"/>.
             </p>
-            <figure xml:id="fig_seq1c" vshift="-2">
-              <caption>Plotting the sequence in <xref ref="item_ex_seq1_3"/></caption>
+            <figure xml:id="fig_seq1c" vshift="-1">
+              <caption>Plotting the sequence in <xref ref="item_ex_seq1_3"/> of <xref ref="ex_seq1"/></caption>
         <!-- START figures/fig_seq1c.tex -->
               <image width="47%">
                 <shortdescription>A plot of the first four terms of the sequence in part 3 of this example.</shortdescription>
@@ -342,7 +342,7 @@
               <m>\{c_n\}=\{1, 1, 2, 6, 24, 120, 720, \ldots\}</m>
             </p>
           </li>
-          <pagebreak-latex component="novideo"/>
+
           <li>
             <p>
               <m>\{d_n\}=\left\{\frac52, \frac52, \frac{15}8, \frac54,\frac{25}{32},\ldots\right\}</m>
@@ -614,8 +614,8 @@
               ranging from about <m>-73</m> to <m>125</m>,
               but as <m>n</m> grows, the values approach 3.
             </p>
-            <figure xml:id="fig_seq4a" vshift="-3">
-              <caption>Scatter plot for the sequence in <xref ref="item_ex_seq4_1"/></caption>
+            <figure xml:id="fig_seq4a" vshift="0.5">
+              <caption>Scatter plot for the sequence in <xref ref="item_ex_seq4_1"/> of <xref ref="ex_seq4"/></caption>
               <!-- START figures/fig_seq4a.tex -->
               <image width="47%">
                 <shortdescription>A scatter plot showing a representative sample of points from the first sequence in this example.</shortdescription>
@@ -681,8 +681,8 @@
               As the sequence takes on values near 1 and <m>-1</m> infinitely many times,
               we conclude that <m>\lim\limits_{n\to\infty}a_n</m> does not exist.
             </p>
-            <figure xml:id="fig_seq4b" vshift="-3">
-              <caption>Scatter plot for the sequence in <xref ref="item_ex_seq4_2"/></caption>
+            <figure xml:id="fig_seq4b" vshift="0.5">
+              <caption>Scatter plot for the sequence in <xref ref="item_ex_seq4_2"/> of <xref ref="ex_seq4"/></caption>
               <!-- START figures/fig_seq4b.tex -->
               <image width="47%">
                 <shortdescription>A scatter plot showing a representative sample of points from the second sequence in this example.</shortdescription>
@@ -730,22 +730,9 @@
               we invoke the definition of the limit of a sequence.
               By looking at the plot in <xref ref="fig_seq4c"/>,
               we would like to conclude that the sequence converges to <m>L=0</m>.
-              Let <m>\epsilon\gt 0</m> be given.
-              We can find a natural number <m>m</m> such that <m>1/m \lt  \varepsilon</m>.
-              Let <m>n\gt m</m>, and consider <m>\abs{a_n - L}</m>:
-              <md>
-                <mrow>\abs{a_n - L} \amp = \left\lvert\frac{(-1)^n}{n} - 0\right\rvert</mrow>
-                <mrow>\amp = \frac1n</mrow>
-                <mrow>\amp \lt  \frac1m \text{ (since \(n\gt m\)) }</mrow>
-                <mrow>\amp \lt  \varepsilon</mrow>
-              </md>.
-              We have shown that by picking <m>m</m> large enough,
-              we can ensure that <m>a_n</m> is arbitrarily close to our limit,
-              <m>L=0</m>,
-              hence by the definition of the limit of a sequence,
-              we can say <m>\lim\limits_{n\to\infty}a_n = 0</m>.
             </p>
-            <figure xml:id="fig_seq4c" vshift="-5">
+
+            <figure xml:id="fig_seq4c" vshift="-3">
               <caption>Scatter plot for the sequence in <xref ref="item_ex_seq4_3"/></caption>
               <!-- START figures/fig_seq4c.tex -->
               <image width="47%">
@@ -788,6 +775,23 @@
               </image>
               <!-- figures/fig_seq4c.tex END -->
             </figure>
+
+            <p>
+              Let <m>\epsilon\gt 0</m> be given.
+              We can find a natural number <m>m</m> such that <m>1/m \lt  \varepsilon</m>.
+              Let <m>n\gt m</m>, and consider <m>\abs{a_n - L}</m>:
+              <md>
+                <mrow>\abs{a_n - L} \amp = \left\lvert\frac{(-1)^n}{n} - 0\right\rvert</mrow>
+                <mrow>\amp = \frac1n</mrow>
+                <mrow>\amp \lt  \frac1m \text{ (since \(n\gt m\)) }</mrow>
+                <mrow>\amp \lt  \varepsilon</mrow>
+              </md>.
+              We have shown that by picking <m>m</m> large enough,
+              we can ensure that <m>a_n</m> is arbitrarily close to our limit,
+              <m>L=0</m>,
+              hence by the definition of the limit of a sequence,
+              we can say <m>\lim\limits_{n\to\infty}a_n = 0</m>.
+            </p>
           </li>
         </ol>
       </p>
@@ -887,7 +891,6 @@
               Because of the alternating nature of this sequence (<ie/>, every other term is multiplied by <m>-1</m>),
               we cannot simply look at the limit <m>\lim\limits_{x\to\infty} \frac{(-1)^x(x+1)}{x}</m>.
               We can try to apply the techniques of <xref ref="thm_abs_val_seq"/>:
-              <pagebreak-latex component="novideo"/>
               <md>
                 <mrow>\lim_{n\to\infty} \abs{a_n} \amp = \lim_{n\to\infty} \abs{\frac{(-1)^n(n+1)}{n}}</mrow>
                 <mrow>\amp = \lim_{n\to\infty} \frac{n+1}{n}</mrow>
@@ -1904,7 +1907,7 @@
 
         <introduction>
           <p>
-            In the following exercises, give the first five terms of the given sequence.
+            Give the first five terms of the given sequence.
           </p>
         </introduction>
 
@@ -1982,8 +1985,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            determine the <m>n</m>th term of the given sequence.
+            Determine the <m>n</m>th term of the given sequence.
           </p>
         </introduction>
 
@@ -2060,8 +2062,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            use the following information to determine the limit of the given sequences.
+            Use the following information to determine the limit of the given sequences.
           </p>
 
           <p>
@@ -2163,8 +2164,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            determine whether the sequence converges or diverges.
+            Determine whether the sequence converges or diverges.
             If convergent, give the limit of the sequence.
           </p>
         </introduction>
@@ -2379,7 +2379,7 @@
 
         <introduction>
           <p>
-            In the following exercises, determine whether the sequence is bounded,
+            Determine whether the sequence is bounded,
             bounded above, bounded below, or none of the above.
           </p>
         </introduction>
@@ -2491,8 +2491,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            determine whether the sequence is monotonically increasing or decreasing.
+            Determine whether the sequence is monotonically increasing or decreasing.
             If it is not,
             determine if there is an <m>m</m> such that it is monotonic for all <m>n\geq m</m>.
           </p>
diff --git a/ptx/sec_series.ptx b/ptx/sec_series.ptx
index 4232ddaea..bba19d7cc 100644
--- a/ptx/sec_series.ptx
+++ b/ptx/sec_series.ptx
@@ -725,9 +725,9 @@
     </example>
   </subsection>
 
-  <pagebreak-latex/>
+  <!-- <pagebreak-latex/> -->
 
-  <subsection>
+  <subsection xml:id="subsec-series">
     <title><m>p</m>-Series</title>
     <p>
       Another important type of series is the <em>p-series</em>.
@@ -1891,7 +1891,7 @@
 
         <introduction>
           <p>
-            In the following exercises, a series <m>\ds\infser a_n</m> is given.
+            A series <m>\ds\infser a_n</m> is given.
           </p>
 
           <p>
@@ -2149,8 +2149,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            use <xref ref="thm_series_nth_term"/>
+            Use <xref ref="thm_series_nth_term"/>
             to show the given series diverges.
           </p>
         </introduction>
@@ -2268,8 +2267,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            state whether the given series converges or diverges.
+            State whether the given series converges or diverges.
           </p>
         </introduction>
 
@@ -2454,7 +2452,7 @@
 
         <introduction>
           <p>
-            In the following exercises, a series is given.
+            A series is given.
           </p>
 
           <p>
diff --git a/ptx/sec_shell_method.ptx b/ptx/sec_shell_method.ptx
index 2b08f0897..a206d5306 100644
--- a/ptx/sec_shell_method.ptx
+++ b/ptx/sec_shell_method.ptx
@@ -1440,7 +1440,7 @@
     We end this section with a table summarizing the usage of the Washer and Shell Methods.
   </p>
 
-  <pagebreak-latex/>
+  <!-- <pagebreak-latex/> -->
 
   <insight xml:id="idea_shell_and_washer">
     <title>Summary of the Washer and Shell Methods</title>
diff --git a/ptx/sec_space_coord.ptx b/ptx/sec_space_coord.ptx
index 08e9a6a42..93eb2cd27 100644
--- a/ptx/sec_space_coord.ptx
+++ b/ptx/sec_space_coord.ptx
@@ -146,7 +146,7 @@
           <idx><h>first octant</h></idx>
     </p>
 
-    <figure xml:id="fig_cartcoord2" vshift="4">
+    <figure xml:id="fig_cartcoord2" vshift="3">
       <caption>Plotting the point <m>P=(2,1,3)</m> in space with a perspective used in this text</caption>
       <!-- START figures/figcartcoord2_3D.asy -->
       <image width="47%">
@@ -4450,8 +4450,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            describe the region in space defined by the inequalities.
+            Describe the region in space defined by the inequalities.
           </p>
         </introduction>
 
@@ -4538,7 +4537,7 @@
 
         <introduction>
           <p>
-            In the following exercises, sketch the cylinder in space.
+            Sketch the cylinder in space.
           </p>
         </introduction>
 
@@ -4898,8 +4897,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            give the equation of the surface of revolution described.
+            Give the equation of the surface of revolution described.
           </p>
         </introduction>
 
@@ -4989,7 +4987,7 @@
 
         <introduction>
           <p>
-            In the following exercises, a quadric surface is sketched.
+            A quadric surface is sketched.
             Determine which of the given equations best fits the graph.
           </p>
         </introduction>
@@ -5315,7 +5313,7 @@
 
         <introduction>
           <p>
-            In the following exercises, sketch the quadric surface.
+            Sketch the quadric surface.
           </p>
         </introduction>
 
diff --git a/ptx/sec_stokes_divergence.ptx b/ptx/sec_stokes_divergence.ptx
index bdfd86ba0..873a934a5 100644
--- a/ptx/sec_stokes_divergence.ptx
+++ b/ptx/sec_stokes_divergence.ptx
@@ -234,11 +234,12 @@
           meaning <em>to the outside</em>, of <m>\surfaceS</m>.)
           The flux across <m>\surfaceS_1</m> is:
           <md>
-            <mrow>\text{ Flux across }\surfaceS_1:\,   \amp = \iint_{\surfaceS_1} \vec F\cdot \vec n_1\, dS</mrow>
-            <mrow>\amp = \int_0^1\int_{-1}^1 \vec F\big(\vec r_1(u,v)\big)\cdot \big(\vec r_{1v}\times\vec r_{1u}\big)\, du\, dv</mrow>
-            <mrow>\amp = \int_0^1\int_{-1}^1 \la v(1-u^2)+u, u^2,4v(1-u^2)\ra \cdot \la 2(u^2-1),0,1-u^2\ra\, du\, dv</mrow>
-            <mrow>\amp = \int_0^1\int_{-1}^1 \big(2u^4v+2u^3-4u^2v-2u+2v\big)\, du\, dv</mrow>
-            <mrow>\amp = \frac{16}{15}</mrow>
+            <mrow>\amp \text{ Flux across }\surfaceS_1:</mrow>
+            <mrow>\amp \quad = \iint_{\surfaceS_1} \vec F\cdot \vec n_1\, dS</mrow>
+            <mrow>\amp \quad = \int_0^1\int_{-1}^1 \vec F\big(\vec r_1(u,v)\big)\cdot \big(\vec r_{1v}\times\vec r_{1u}\big)\, du\, dv</mrow>
+            <mrow>\amp \quad = \int_0^1\int_{-1}^1 \la v(1-u^2)+u, u^2,4v(1-u^2)\ra \cdot \la 2(u^2-1),0,1-u^2\ra\, du\, dv</mrow>
+            <mrow>\amp \quad = \int_0^1\int_{-1}^1 \big(2u^4v+2u^3-4u^2v-2u+2v\big)\, du\, dv</mrow>
+            <mrow>\amp \quad = \frac{16}{15}</mrow>
           </md>.
         </p>
 
@@ -249,11 +250,12 @@
           meaning this vector points outside <m>\surfaceS</m>.)
           The flux across <m>\surfaceS_2</m> is:
           <md>
-            <mrow>\text{ Flux across } \surfaceS_2:\,  \amp = \iint_{\surfaceS_2} \vec F\cdot \vec n_2\, dS</mrow>
-            <mrow>\amp = \int_0^1\int_{-1}^1 \vec F\big(\vec r_2(u,v)\big)\cdot \big(\vec r_{2u}\times\vec r_{2v}\big)\, du\, dv</mrow>
-            <mrow>\amp = \int_0^1\int_{-1}^1 \la 1-u^2+u, u^2, 4v(1-u^2)\ra \cdot \la 2(1-u^2), 4u(1-u^2),0\ra\, du\, dv</mrow>
-            <mrow>\amp = \int_0^1\int_{-1}^1 \big(4u^5-2u^4-2u^3+4u^2-2u-2\big)\, du\, dv</mrow>
-            <mrow>\amp = \frac{32}{15}</mrow>
+            <mrow>\amp \text{ Flux across } \surfaceS_2:</mrow>
+            <mrow>\amp \quad = \iint_{\surfaceS_2} \vec F\cdot \vec n_2\, dS</mrow>
+            <mrow>\amp \quad = \int_0^1\int_{-1}^1 \vec F\big(\vec r_2(u,v)\big)\cdot \big(\vec r_{2u}\times\vec r_{2v}\big)\, du\, dv</mrow>
+            <mrow>\amp \quad = \int_0^1\int_{-1}^1 \la 1-u^2+u, u^2, 4v(1-u^2)\ra \cdot \la 2(1-u^2), 4u(1-u^2),0\ra\, du\, dv</mrow>
+            <mrow>\amp \quad = \int_0^1\int_{-1}^1 \big(4u^5-2u^4-2u^3+4u^2-2u-2\big)\, du\, dv</mrow>
+            <mrow>\amp \quad = \frac{32}{15}</mrow>
           </md>.
         </p>
 
@@ -264,11 +266,12 @@
           meaning this vector points down, outside of <m>\surfaceS</m>.)
           The flux across <m>\surfaceS_3</m> is:
           <md>
-            <mrow>\text{ Flux across } \surfaceS_3:\,  \amp = \iint_{\surfaceS_3} \vec F\cdot \vec n_3\, dS</mrow>
-            <mrow>\amp = \int_0^1\int_{-1}^1 \vec F\big(\vec r_3(u,v)\big)\cdot \big(\vec r_{3u}\times\vec r_{3v}\big)\, du\, dv</mrow>
-            <mrow>\amp = \int_0^1\int_{-1}^1 \la v(1-u^2)+u,u^2,0\ra \cdot \la 0,0,u^2-1\ra\, du\, dv</mrow>
-            <mrow>\amp = \int_0^1\int_{-1}^1 0\, du\, dv</mrow>
-            <mrow>\amp = 0</mrow>
+            <mrow>\amp\text{ Flux across } \surfaceS_3:</mrow>
+            <mrow>\amp \quad = \iint_{\surfaceS_3} \vec F\cdot \vec n_3\, dS</mrow>
+            <mrow>\amp \quad = \int_0^1\int_{-1}^1 \vec F\big(\vec r_3(u,v)\big)\cdot \big(\vec r_{3u}\times\vec r_{3v}\big)\, du\, dv</mrow>
+            <mrow>\amp \quad = \int_0^1\int_{-1}^1 \la v(1-u^2)+u,u^2,0\ra \cdot \la 0,0,u^2-1\ra\, du\, dv</mrow>
+            <mrow>\amp \quad = \int_0^1\int_{-1}^1 0\, du\, dv</mrow>
+            <mrow>\amp \quad = 0</mrow>
           </md>.
         </p>
 
@@ -702,6 +705,8 @@
           </md>.
         </p>
 
+        <enlarge-page skipsize="2"/>
+
         <p>
           The direct flux computation requires six surface integrals,
           one for each face of the cube.
@@ -787,7 +792,7 @@
           Verify Stoke's Theorem by showing <m>\oint_C \vec F\cdot \, d\vec r = \iint_\surfaceS (\curl\vec F)\cdot \vec n\, dS</m>.
         </p>
 
-        <figure xml:id="fig_stokes1" vshift="0">
+        <figure xml:id="fig_stokes1" vshift="2">
           <caption>As given in <xref ref="ex_stokes1"/>, the surface <m>\surfaceS</m><nbsp/>is the portion of the plane bounded by the curve</caption>
           <image width="47%">
             <shortdescription>An ellipse drawn on a plane in space. It lies over a circle in the x,y plane.</shortdescription>
@@ -1141,7 +1146,7 @@
     </figure>
   </subsection>
 
-  <subsection>
+  <subsection xml:id="subsec-common-thread">
     <title>A Common Thread of Calculus</title>
     <p>
       We have threefold interest in each of the major theorems of this chapter:
@@ -1286,8 +1291,7 @@
       <exercisegroup cols="2" xml:id="exset-divergence-theorem-verify">
         <introduction>
           <p>
-            In the following exercises,
-            a closed surface <m>\surfaceS</m> enclosing a domain <m>D</m> and a vector field <m>\vec F</m> are given.
+            A closed surface <m>\surfaceS</m> enclosing a domain <m>D</m> and a vector field <m>\vec F</m> are given.
             Verify the Divergence Theorem on <m>\surfaceS</m>; that is,
             show <m>\iint_\surfaceS \vec F\cdot \vec n\, dS = \iiint_D\divv \vec F\, dV</m>.
           </p>
@@ -1733,8 +1737,7 @@
       <exercisegroup cols="2" xml:id="exset-stokes-theorem-verify">
         <introduction>
           <p>
-            In the following exercises,
-            a closed curve <m>C</m> that is the boundary of a surface <m>\surfaceS</m> is given along with a vector field <m>\vec F</m>.
+            A closed curve <m>C</m> that is the boundary of a surface <m>\surfaceS</m> is given along with a vector field <m>\vec F</m>.
             Verify Stokes' Theorem on <m>C</m>;
             that is, show <m>\oint_C \vec F\cdot d\vec r = \iint_\surfaceS\big(\curl \vec F\,\big)\cdot\vec n\, dS</m>.
           </p>
@@ -2109,8 +2112,7 @@
       <exercisegroup cols="2" xml:id="exset-divergence-theorem-flux">
         <introduction>
           <p>
-            In the following exercises,
-            a closed surface <m>\surfaceS</m> and a vector field <m>\vec F</m> are given.
+            A closed surface <m>\surfaceS</m> and a vector field <m>\vec F</m> are given.
             Find the outward flux of <m>\vec F</m> over <m>\surfaceS</m> either through direct computation or through the Divergence Theorem.
           </p>
         </introduction>
@@ -2575,8 +2577,7 @@
       <exercisegroup cols="2" xml:id="exset-stokes-theorem-circulation">
         <introduction>
           <p>
-            In the following exercises,
-            a closed curve <m>C</m> that is the boundary of a surface <m>\surfaceS</m> is given along with a vector field <m>\vec F</m>.
+            A closed curve <m>C</m> that is the boundary of a surface <m>\surfaceS</m> is given along with a vector field <m>\vec F</m>.
             Find the circulation of <m>\vec F</m> around <m>C</m> either through direct computation or through Stokes' Theorem.
           </p>
         </introduction>
diff --git a/ptx/sec_surface_area.ptx b/ptx/sec_surface_area.ptx
index ea03069ca..0262eacac 100644
--- a/ptx/sec_surface_area.ptx
+++ b/ptx/sec_surface_area.ptx
@@ -932,8 +932,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            <em>set up</em> the iterated integral that computes the surface area of the graph of the given function over the region <m>R</m>.
+            <em>Set up</em> the iterated integral that computes the surface area of the graph of the given function over the region <m>R</m>.
           </p>
         </introduction>
 
@@ -1270,8 +1269,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the area of the given surface over the region <m>R</m>.
+            Find the area of the given surface over the region <m>R</m>.
           </p>
         </introduction>
 
diff --git a/ptx/sec_surface_integral.ptx b/ptx/sec_surface_integral.ptx
index 7369a2f5c..72cf716ad 100644
--- a/ptx/sec_surface_integral.ptx
+++ b/ptx/sec_surface_integral.ptx
@@ -866,8 +866,7 @@
       <exercisegroup cols="2" xml:id="exset-surface-area-mass">
         <introduction>
           <p>
-            In the following exercises,
-            a surface <m>\surfaceS</m> that represents a thin sheet of material with density <m>\delta</m> is given.
+            A surface <m>\surfaceS</m> that represents a thin sheet of material with density <m>\delta</m> is given.
             Find the mass of each thin sheet.
           </p>
         </introduction>
@@ -906,8 +905,7 @@
       <exercisegroup cols="2" xml:id="exset-surface-integral-flux">
         <introduction>
           <p>
-            In the following exercises,
-            a surface <m>\surfaceS</m> and a vector field <m>\vec F</m> are given.
+            A surface <m>\surfaceS</m> and a vector field <m>\vec F</m> are given.
             Compute the flux of <m>\vec F</m> across <m>\surfaceS</m>.
             (If <m>\surfaceS</m> is not a closed surface,
             choose <m>\vec n</m> so that it has a positive <m>z</m>-component,
diff --git a/ptx/sec_tan_norm.ptx b/ptx/sec_tan_norm.ptx
index 260a1eb0c..6f2293ae0 100644
--- a/ptx/sec_tan_norm.ptx
+++ b/ptx/sec_tan_norm.ptx
@@ -68,7 +68,7 @@
           since they are only length 1.)
         </p>
 
-        <figure xml:id="fig_tannorm1" vshift="-3">
+        <figure xml:id="fig_tannorm1" vshift="-1">
           <caption>Plotting unit tangent vectors in <xref ref="ex_tannorm1"/></caption>
 
           <!-- START figures/figtannorm1_3D.asy -->
@@ -186,7 +186,7 @@
           They are plotted in <xref ref="fig_tannorm2"/>
         </p>
 
-        <figure xml:id="fig_tannorm2" vshift="0">
+        <figure xml:id="fig_tannorm2" vshift="2">
           <caption>Plotting unit tangent vectors in <xref ref="ex_tannorm2"/></caption>
           <!-- START figures/fig_tannorm2.tex -->
           <image width="47%">
@@ -250,7 +250,7 @@
       It is good to wonder <q>Is one of these two directions preferable over the other?</q>
     </p>
 
-    <figure xml:id="fig_tannorm_intro1" vshift="-2">
+    <figure xml:id="fig_tannorm_intro1" vshift="0">
       <caption>Given a direction in the plane, there are always two directions orthogonal to it</caption>
       <!-- START figures/fig_tannorm_intro1.tex -->
       <image width="47%">
@@ -382,8 +382,8 @@
           These are sketched in <xref ref="fig_tannorm3"/>.
         </p>
 
-        <figure xml:id="fig_tannorm3" vshift="-2">
-          <caption>Plotting unit tangent and normal vectors in <xref ref="fig_tannorm3"/></caption>
+        <figure xml:id="fig_tannorm3" vshift="0">
+          <caption>Plotting unit tangent and normal vectors in <xref ref="ex_tannorm3"/></caption>
 
           <!-- START figures/figtannorm3_3D.asy -->
           <image width="47%">
@@ -447,7 +447,7 @@
       </solution>
     </example>
 
-    <aside vshift="-1">
+    <aside vshift="-6">
       <p>
         There is one flaw in our definition of <m>\unitnormal(t)</m>:
         it is possible that we could have <m>\unittangentprime(t)=0</m>!
@@ -665,7 +665,7 @@
       The following theorem gives alternate formulas for
       <m>a_\text{T}</m> and <m>a_\text{N}</m>.
     </p>
-    <aside vshift="0">
+    <aside vshift="1">
       <p>
         Keep in mind that both <m>a_\text{T}</m> and
         <m>a_\text{N}</m> are functions of <m>t</m>;
@@ -802,7 +802,7 @@
           gives a graph of the path for reference.
         </p>
 
-        <figure xml:id="fig_tannorm6" vshift="-2">
+        <figure xml:id="fig_tannorm6" vshift="0">
           <caption>Graphing <m>\vec r(t)</m> in <xref ref="ex_tannorm6"/></caption>
           <!-- START figures/fig_tannorm6.tex -->
           <image width="47%">
@@ -1353,8 +1353,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find <m>\unitnormal(t)</m> using <xref ref="def_unit_normal"/>.
+            Find <m>\unitnormal(t)</m> using <xref ref="def_unit_normal"/>.
             Confirm the result using <xref ref="thm_concave"/>.
           </p>
         </introduction>
@@ -1436,8 +1435,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            a position function <m>\vrt</m> is given along with its unit tangent vector
+            A position function <m>\vrt</m> is given along with its unit tangent vector
             <m>\unittangent(t)</m> evaluated at <m>t=a</m>,
             for some value of <m>a</m>.
           </p>
@@ -1581,7 +1579,7 @@
 
         <introduction>
           <p>
-            In the following exercises, find <m>\unitnormal(t)</m>.
+            Find <m>\unitnormal(t)</m>.
           </p>
         </introduction>
 
@@ -1669,8 +1667,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find <m>a_\text{T}</m> and <m>a_\text{N}</m> given <m>\vrt</m>.
+            Find <m>a_\text{T}</m> and <m>a_\text{N}</m> given <m>\vrt</m>.
             Be sure you can sketch <m>\vrt</m> on the indicated interval,
             and comment on the relative sizes of <m>a_\text{T}</m> and
             <m>a_\text{N}</m> at the indicated <m>t</m> values.
diff --git a/ptx/sec_taylor_poly.ptx b/ptx/sec_taylor_poly.ptx
index fb8185770..2be67c0e3 100644
--- a/ptx/sec_taylor_poly.ptx
+++ b/ptx/sec_taylor_poly.ptx
@@ -351,7 +351,6 @@
       <xref ref="fig_taypolyintroc"/> shows <m>p_{13}(x)</m>;
       we can visually affirm that this polynomial approximates <m>f</m> very
       well on <m>[-2,3]</m>. 
-      <pagebreak-latex component="taypoly-late"/>
       The polynomial <m>p_{13}(x)</m> is not
       particularly <q>nice</q>. It is
       <md>
@@ -2031,8 +2030,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the Maclaurin polynomial of degree <m>n</m> for the given function.
+            Find the Maclaurin polynomial of degree <m>n</m> for the given function.
           </p>
         </introduction>
 
@@ -2424,8 +2422,7 @@
       <exercisegroup cols="2" xml:id="exset-taylor-poly-error-bound">
         <introduction>
           <p>
-            In the following exercises,
-            approximate the function value with the indicated Taylor polynomial
+            Approximate the function value with the indicated Taylor polynomial
             and give approximate bounds on the error.
           </p>
         </introduction>
@@ -2622,8 +2619,7 @@
       <exercisegroup cols="2" xml:id="exset-taylor-poly-nth-term">
         <introduction>
           <p>
-            In the following exercises,
-            find the <m>n</m>th term of the indicated Taylor polynomial.
+            Find the <m>n</m>th term of the indicated Taylor polynomial.
           </p>
         </introduction>
 
@@ -2740,8 +2736,7 @@
       <exercisegroup cols="2" xml:id="exset-taylor-poly-ode">
         <introduction>
           <p>
-            In the following exercises,
-            approximate the solution to the given differential equation with a
+            Approximate the solution to the given differential equation with a
             degree 4 Maclaurin polynomial.
           </p>
         </introduction>
diff --git a/ptx/sec_taylor_series.ptx b/ptx/sec_taylor_series.ptx
index 1f33d6812..b1d8e14fd 100644
--- a/ptx/sec_taylor_series.ptx
+++ b/ptx/sec_taylor_series.ptx
@@ -1316,7 +1316,7 @@
           <p>
             <xref ref="idea_common_taylor" component="taypoly-late"/><xref ref="idea_common_taylor-early" component="taypoly-early"/>
             gives the <m>n</m>th term of the Taylor series of common functions.
-            In the following exercises, verify the formula given in the Key Idea by finding
+            Verify the formula given in the Key Idea by finding
             the first few terms of the Taylor series of the given function and identifying a pattern.
           </p>
         </introduction>
@@ -1443,8 +1443,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find a formula for the <m>n</m>th term of the Taylor series of <m>f(x)</m>,
+            Find a formula for the <m>n</m>th term of the Taylor series of <m>f(x)</m>,
             centered at <m>c</m>,
             by finding the coefficients of the first few powers of <m>x</m> and looking for a pattern.
             (The formulas for several of these are found in <xref ref="idea_common_taylor" component="taypoly-late"/><xref ref="idea_common_taylor-early" component="taypoly-early"/>;
@@ -1613,8 +1612,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            show that the Taylor series for <m>f(x)</m>,
+            Show that the Taylor series for <m>f(x)</m>,
             as given in <xref ref="idea_common_taylor" component="taypoly-late"/><xref ref="idea_common_taylor-early" component="taypoly-early"/>,
             is equal to <m>f(x)</m> by applying <xref ref="thm_function_series_equality"/>;
             that is, show <m>\lim\limits_{n\to\infty}R_n(x) =0</m>.
@@ -1803,8 +1801,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            use the Taylor series given in <xref ref="idea_common_taylor" component="taypoly-late"/><xref ref="idea_common_taylor-early" component="taypoly-early"/> to verify the given identity.
+            Use the Taylor series given in <xref ref="idea_common_taylor" component="taypoly-late"/><xref ref="idea_common_taylor-early" component="taypoly-early"/> to verify the given identity.
           </p>
         </introduction>
 
@@ -1908,8 +1905,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            write out the first 5 terms of the Binomial series with the given <m>k</m>-value.
+            Write out the first 5 terms of the Binomial series with the given <m>k</m>-value.
           </p>
         </introduction>
 
@@ -1987,8 +1983,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            use the Taylor series given in <xref ref="idea_common_taylor" component="taypoly-late"/><xref ref="idea_common_taylor-early" component="taypoly-early"/>
+            Use the Taylor series given in <xref ref="idea_common_taylor" component="taypoly-late"/><xref ref="idea_common_taylor-early" component="taypoly-early"/>
             to create the Taylor series of the given functions.
           </p>
         </introduction>
@@ -2100,8 +2095,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            approximate the value of the given definite integral by using the first 4 nonzero terms of the integrand's Taylor series.
+            Approximate the value of the given definite integral by using the first 4 nonzero terms of the integrand's Taylor series.
           </p>
         </introduction>
 
diff --git a/ptx/sec_total_differential.ptx b/ptx/sec_total_differential.ptx
index e62fc51e6..f74e5fd38 100644
--- a/ptx/sec_total_differential.ptx
+++ b/ptx/sec_total_differential.ptx
@@ -799,7 +799,7 @@
 
         <introduction>
           <p>
-            In the following exercises, find the total differential <m>dz</m>.
+            Find the total differential <m>dz</m>.
           </p>
         </introduction>
 
@@ -880,7 +880,7 @@
 
         <introduction>
           <p>
-            In the following exercises, a function <m>f(x,y)</m> is given.
+            A function <m>f(x,y)</m> is given.
             Give the indicated approximation using the total differential.
           </p>
         </introduction>
@@ -974,302 +974,302 @@
         </exercise>
 
       </exercisegroup>
-      <exercisegroup cols="2" xml:id="exset-total-differential-error-analysis">
+
+      <exercisegroup cols="2" xml:id="exset-total-differential-r3">
 
         <introduction>
           <p>
-            The following exercises ask a variety of questions dealing with approximating error and sensitivity analysis.
+            Find the total differential <m>dw</m>.
           </p>
         </introduction>
 
-        <exercise label="ex-total-differential-error-analysis-1">
-          <!--<webwork xml:id="webwork-ex-total-differential-error-analysis-1">
+        <exercise label="ex-total-differential-r3-1">
+          <!--<webwork xml:id="webwork-ex-total-differential-r3-1">
               <pg-code>
               </pg-code>
               -->
               <statement>
                 <p>
-                  A cylindrical storage tank is to be 2ft tall with a radius of 1ft.
-                  Is the volume of the tank more sensitive to changes in the radius or the height?
+                  <m>w= x^2yz^3</m>
                 </p>
               </statement>
               <solution>
                 <p>
-                  The total differential of volume is <m>dV = 4\pi dr + \pi dh</m>.
-                  The coefficient of <m>dr</m> is greater than the coefficient of <m>dh</m>,
-                  so the volume is more sensitive to changes in the radius.
+                  <m>dw = 2xyz^3\,dx + x^2z^3\,dy + 3x^2yz^2\,dz</m>
                 </p>
               </solution>
           <!--</webwork>-->
         </exercise>
 
-        <exercise label="ex-total-differential-error-analysis-2">
-          <!--<webwork xml:id="webwork-ex-total-differential-error-analysis-2">
+        <exercise label="ex-total-differential-r3-2">
+          <!--<webwork xml:id="webwork-ex-total-differential-r3-2">
               <pg-code>
               </pg-code>
               -->
               <statement>
                 <p>
-                  <em>Projectile Motion:</em> The <m>x</m>-value of an object moving under the principles of projectile motion is <m>x(\theta,v_0,t)= (v_0\cos(\theta) )t</m>.
-                  A particular projectile is fired with an initial velocity of <m>v_0=250</m>ft/s and an angle of elevation of <m>\theta = 60^\circ</m>.
-                  It travels a distance of <m>375</m>ft in 3 seconds.
-                </p>
-
-                <p>
-                  Is the projectile more sensitive to errors in initial speed or angle of elevation?
+                  <m>w= e^x\sin(y) \ln(z)</m>
                 </p>
               </statement>
               <solution>
                 <p>
-                  Distance of the projectile is a function of two variables (leaving <m>t=3</m>):
-                  <m>D(v_0,\theta) = 3v_0\cos(\theta)</m>.
-                  The total differential of <m>D</m> is <m>dD = 3\cos(\theta) dv_0-3v_0\sin(\theta) d\theta</m>.
-                  The coefficient of <m>d\theta</m> has a much greater magnitude than the coefficient of <m>dv_0</m>,
-                  so a small change in the angle of elevation has a much greater effect on distance traveled than a small change in initial velocity.
+                  <m>dw = e^x\sin(y) \ln(z) \,dx + e^x\cos(y) \ln(z) \,dy + e^x\sin(y) \frac1z\,dz</m>
                 </p>
               </solution>
           <!--</webwork>-->
         </exercise>
 
-        <exercise label="ex-total-differential-error-analysis-3">
-          <!--<webwork xml:id="webwork-ex-total-differential-error-analysis-3">
+      </exercisegroup>
+      <exercisegroup cols="2" xml:id="exset-total-differential-approx-from-data">
+
+        <introduction>
+          <p>
+            Use the information provided and the total differential to make the given approximation.
+          </p>
+        </introduction>
+
+        <exercise label="ex-total-differential-approx-from-data-1">
+          <!--<webwork xml:id="webwork-ex-total-differential-approx-from-data-1">
               <pg-code>
               </pg-code>
               -->
               <statement>
                 <p>
-                  The length <m>\ell</m> of a long wall is to be approximated.
-                  The angle <m>\theta</m>, as shown in the diagram
-                  (not to scale),
-                  is measured to be <m>85^\circ</m>,
-                  and the distance <m>x</m> is measured to be 30'. Assume that the triangle formed is a right triangle.
-                </p>
-
-                <p>
-                  Is the measurement of the length of <m>\ell</m> more sensitive to errors in the measurement of <m>x</m> or in <m>\theta</m>?
+                  <m>f(3,1) = 7</m>,<nbsp/>
+                  <m>f_x(3,1) = 9</m>, <m>f_y(3,1) = -2</m>.
+                  Approximate <m>f(3.05, 0.9)</m>.
                 </p>
-
-                <image width="60%">
-                  <shortdescription>A right-angled triangle illustrating a wall of unknown height, a horizontal distance, and an angle.</shortdescription>
-                  <description>
-                    <p>
-                      The diagram illustrates a simple right-angled triangle. 
-                      The base of the triangle is labeled <m>x</m>. The height of the triangle is labeled <m>\ell</m>.
-                      The angle opposite the wall is labeled <m>\theta</m>.
-                    </p>
-                  </description>
-                  <latex-image label="img_ex15">
-
-                  \begin{tikzpicture}
-
-                  \draw [ultra thick] (1,-1) -- node [pos=.5,right] { \(\ell=\)?}(1,1);
-                  \draw [dashed] (1,1) -- (-1,-1) node [xshift=10pt,yshift=5pt] { \(\theta\)} -- node [pos=.5,below] { \(x\)} (1,-1);
-
-                  \end{tikzpicture}
-
-                  </latex-image>
-                </image>
               </statement>
               <solution>
                 <p>
-                  Using trigonometry, <m>\ell = x\tan(\theta)</m>,
-                  so <m>d\ell = \tan(\theta) dx + x\sec^2(\theta) d\theta</m>.
-                  With <m>\theta = 85^\circ</m> and <m>x=30</m>,
-                  we have <m>d\ell = 11.43dx+3949.38d\theta</m>.
-                  The measured length of the wall is much more sensitive to errors in <m>\theta</m> than in <m>x</m>.
-                  While it can be difficult to compare sensitivities between measuring feet and measuring degrees
-                  (it is somewhat like <q>comparing apples to oranges</q>),
-                  here the coefficients are so different that the result is clear:
-                  a small error in degree has a much greater impact than a small error in distance.
+                  <m>dx = 0.05</m>, <m>dy = -0.1</m>.
+                  <m>dz = 9(.05)+(-2)(-0.1) = 0.65</m>.
+                  So <m>f(3.05,0.9) \approx 7+0.65=7.65</m>.
                 </p>
               </solution>
           <!--</webwork>-->
         </exercise>
 
-        <exercise label="ex-total-differential-error-analysis-4">
-          <!--<webwork xml:id="webwork-ex-total-differential-error-analysis-4">
+        <exercise label="ex-total-differential-approx-from-data-2">
+          <!--<webwork xml:id="webwork-ex-total-differential-approx-from-data-2">
               <pg-code>
               </pg-code>
               -->
               <statement>
                 <p>
-                  It is <q>common sense</q> that it is far better to measure a long distance with a long measuring tape rather than a short one.
-                  A measured distance <m>D</m> can be viewed as the product of the length <m>\ell</m> of a measuring tape times the number <m>n</m> of times it was used.
-                  For instance,
-                  using a 3' tape 10 times gives a length of 30'. To measure the same distance with a 12' tape,
-                  we would use the tape 2.5 times. (<ie/>,
-                  <m>30=12\times 2.5</m>.) Thus <m>D = n\ell</m>.
-                </p>
-
-                <p>
-                  Suppose each time a measurement is taken with the tape,
-                  the recorded distance is within 1/16'' of the actual distance. (<ie/>, <m>d\ell = 1/16'' \approx 0.005</m>ft).
-                  Using differentials,
-                  show why common sense proves correct in that it is better to use a long tape to measure long distances.
+                  <m>f(-4,2) = 13</m>,<nbsp/>
+                  <m>f_x(-4,2) = 2.6</m>, <m>f_y(-4,2) = 5.1</m>.
+                  Approximate <m>f(-4.12, 2.07)</m>.
                 </p>
               </statement>
               <solution>
                 <p>
-                  With <m>D = n\ell</m>,
-                  the total differential is <m>dD = \ell\, dn+ n\,d\ell</m>.
-                  If one measures with a short tape,
-                  <m>n</m> must be large and hence
-                  <m>n\,d\ell</m> is going to be greater than when a large tape is used
-                  (wherein <m>n</m> will be small).
+                  <m>dx = -0.12</m>, <m>dy = 0.07</m>.
+                  <m>dz = 2.6(-.12)+(5.1)(0.07) = 0.045</m>.
+                  So <m>f(-4.12, 2.07) \approx 13+0.045=13.045</m>.
                 </p>
               </solution>
           <!--</webwork>-->
         </exercise>
 
-      </exercisegroup>
-      <exercisegroup cols="2" xml:id="exset-total-differential-r3">
-
-        <introduction>
-          <p>
-            In the following exercises, find the total differential <m>dw</m>.
-          </p>
-        </introduction>
-
-        <exercise label="ex-total-differential-r3-1">
-          <!--<webwork xml:id="webwork-ex-total-differential-r3-1">
+        <exercise label="ex-total-differential-approx-from-data-3">
+          <!-- <webwork xml:id="webwork-ex-total-differential-approx-from-data-3">
               <pg-code>
               </pg-code>
-              -->
+               -->
               <statement>
                 <p>
-                  <m>w= x^2yz^3</m>
+                  <m>f(2,4,5) = -1</m>,<nbsp/> <m>f_x(2,4,5) = 2</m>,<nbsp/>
+                  <m>f_y(2,4,5) = -3</m>,<nbsp/> <m>f_z(2,4,5) = 3.7</m>.
+                  Approximate <m>f(2.5,4.1,4.8)</m>.
                 </p>
               </statement>
               <solution>
                 <p>
-                  <m>dw = 2xyz^3\,dx + x^2z^3\,dy + 3x^2yz^2\,dz</m>
+                  <m>dx = 0.5</m>, <m>dy = 0.1</m>, <m>dz = -0.2</m>.
+                </p>
+
+                <p>
+                  <m>dw = 2(0.5) + (-3)(0.1) + 3.7(-0.2) = -0.04</m>,
+                  so <m>f(2.5, 4.1, 4.8) \approx -1-0.04 = -1.04</m>.
                 </p>
               </solution>
           <!--</webwork>-->
         </exercise>
 
-        <exercise label="ex-total-differential-r3-2">
-          <!--<webwork xml:id="webwork-ex-total-differential-r3-2">
+        <exercise label="ex-total-differential-approx-from-data-4">
+          <!--<webwork xml:id="webwork-ex-total-differential-approx-from-data-4">
               <pg-code>
               </pg-code>
               -->
               <statement>
                 <p>
-                  <m>w= e^x\sin(y) \ln(z)</m>
+                  <m>f(3,3,3) = 5</m>,<nbsp/> <m>f_x(3,3,3) = 2</m>,<nbsp/>
+                  <m>f_y(3,3,3) = 0</m>,<nbsp/> <m>f_z(3,3,3) = -2</m>.
+                  Approximate <m>f(3.1, 3.1,3.1)</m>.
                 </p>
               </statement>
               <solution>
                 <p>
-                  <m>dw = e^x\sin(y) \ln(z) \,dx + e^x\cos(y) \ln(z) \,dy + e^x\sin(y) \frac1z\,dz</m>
+                  <m>dx = 0.1</m>, <m>dy = 0.1</m>, <m>dz = 0.1</m>.
+                </p>
+
+                <p>
+                  <m>dw = 2(0.1) + (0)(0.1) + (-2)(.1) = 0</m>,
+                  so <m>f(3.1,3.1,3.1) \approx 5+0=5</m>.
                 </p>
               </solution>
           <!--</webwork>-->
         </exercise>
 
       </exercisegroup>
-      <exercisegroup cols="2" xml:id="exset-total-differential-approx-from-data">
+
+            <exercisegroup cols="2" xml:id="exset-total-differential-error-analysis">
 
         <introduction>
           <p>
-            In the following exercises,
-            use the information provided and the total differential to make the given approximation.
+            The following exercises ask a variety of questions dealing with approximating error and sensitivity analysis.
           </p>
         </introduction>
 
-        <exercise label="ex-total-differential-approx-from-data-1">
-          <!--<webwork xml:id="webwork-ex-total-differential-approx-from-data-1">
+        <exercise label="ex-total-differential-error-analysis-1">
+          <!--<webwork xml:id="webwork-ex-total-differential-error-analysis-1">
               <pg-code>
               </pg-code>
               -->
               <statement>
                 <p>
-                  <m>f(3,1) = 7</m>,<nbsp/>
-                  <m>f_x(3,1) = 9</m>, <m>f_y(3,1) = -2</m>.
-                  Approximate <m>f(3.05, 0.9)</m>.
+                  A cylindrical storage tank is to be 2ft tall with a radius of 1ft.
+                  Is the volume of the tank more sensitive to changes in the radius or the height?
                 </p>
               </statement>
               <solution>
                 <p>
-                  <m>dx = 0.05</m>, <m>dy = -0.1</m>.
-                  <m>dz = 9(.05)+(-2)(-0.1) = 0.65</m>.
-                  So <m>f(3.05,0.9) \approx 7+0.65=7.65</m>.
+                  The total differential of volume is <m>dV = 4\pi dr + \pi dh</m>.
+                  The coefficient of <m>dr</m> is greater than the coefficient of <m>dh</m>,
+                  so the volume is more sensitive to changes in the radius.
                 </p>
               </solution>
           <!--</webwork>-->
         </exercise>
 
-        <exercise label="ex-total-differential-approx-from-data-2">
-          <!--<webwork xml:id="webwork-ex-total-differential-approx-from-data-2">
+        <exercise label="ex-total-differential-error-analysis-2">
+          <!--<webwork xml:id="webwork-ex-total-differential-error-analysis-2">
               <pg-code>
               </pg-code>
               -->
               <statement>
                 <p>
-                  <m>f(-4,2) = 13</m>,<nbsp/>
-                  <m>f_x(-4,2) = 2.6</m>, <m>f_y(-4,2) = 5.1</m>.
-                  Approximate <m>f(-4.12, 2.07)</m>.
+                  <em>Projectile Motion:</em> The <m>x</m>-value of an object moving under the principles of projectile motion is <m>x(\theta,v_0,t)= (v_0\cos(\theta) )t</m>.
+                  A particular projectile is fired with an initial velocity of <m>v_0=250</m>ft/s and an angle of elevation of <m>\theta = 60^\circ</m>.
+                  It travels a distance of <m>375</m>ft in 3 seconds.
+                </p>
+
+                <p>
+                  Is the projectile more sensitive to errors in initial speed or angle of elevation?
                 </p>
               </statement>
               <solution>
                 <p>
-                  <m>dx = -0.12</m>, <m>dy = 0.07</m>.
-                  <m>dz = 2.6(-.12)+(5.1)(0.07) = 0.045</m>.
-                  So <m>f(-4.12, 2.07) \approx 13+0.045=13.045</m>.
+                  Distance of the projectile is a function of two variables (leaving <m>t=3</m>):
+                  <m>D(v_0,\theta) = 3v_0\cos(\theta)</m>.
+                  The total differential of <m>D</m> is <m>dD = 3\cos(\theta) dv_0-3v_0\sin(\theta) d\theta</m>.
+                  The coefficient of <m>d\theta</m> has a much greater magnitude than the coefficient of <m>dv_0</m>,
+                  so a small change in the angle of elevation has a much greater effect on distance traveled than a small change in initial velocity.
                 </p>
               </solution>
           <!--</webwork>-->
         </exercise>
 
-        <exercise label="ex-total-differential-approx-from-data-3">
-          <!-- <webwork xml:id="webwork-ex-total-differential-approx-from-data-3">
+        <exercise label="ex-total-differential-error-analysis-3">
+          <!--<webwork xml:id="webwork-ex-total-differential-error-analysis-3">
               <pg-code>
               </pg-code>
-               -->
+              -->
               <statement>
                 <p>
-                  <m>f(2,4,5) = -1</m>,<nbsp/> <m>f_x(2,4,5) = 2</m>,<nbsp/>
-                  <m>f_y(2,4,5) = -3</m>,<nbsp/> <m>f_z(2,4,5) = 3.7</m>.
-                  Approximate <m>f(2.5,4.1,4.8)</m>.
+                  The length <m>\ell</m> of a long wall is to be approximated.
+                  The angle <m>\theta</m>, as shown in the diagram
+                  (not to scale),
+                  is measured to be <m>85^\circ</m>,
+                  and the distance <m>x</m> is measured to be 30'. Assume that the triangle formed is a right triangle.
                 </p>
-              </statement>
-              <solution>
+
                 <p>
-                  <m>dx = 0.5</m>, <m>dy = 0.1</m>, <m>dz = -0.2</m>.
+                  Is the measurement of the length of <m>\ell</m> more sensitive to errors in the measurement of <m>x</m> or in <m>\theta</m>?
                 </p>
 
+                <image width="60%">
+                  <shortdescription>A right-angled triangle illustrating a wall of unknown height, a horizontal distance, and an angle.</shortdescription>
+                  <description>
+                    <p>
+                      The diagram illustrates a simple right-angled triangle. 
+                      The base of the triangle is labeled <m>x</m>. The height of the triangle is labeled <m>\ell</m>.
+                      The angle opposite the wall is labeled <m>\theta</m>.
+                    </p>
+                  </description>
+                  <latex-image label="img_ex15">
+
+                  \begin{tikzpicture}
+
+                  \draw [ultra thick] (1,-1) -- node [pos=.5,right] { \(\ell=\)?}(1,1);
+                  \draw [dashed] (1,1) -- (-1,-1) node [xshift=10pt,yshift=5pt] { \(\theta\)} -- node [pos=.5,below] { \(x\)} (1,-1);
+
+                  \end{tikzpicture}
+
+                  </latex-image>
+                </image>
+              </statement>
+              <solution>
                 <p>
-                  <m>dw = 2(0.5) + (-3)(0.1) + 3.7(-0.2) = -0.04</m>,
-                  so <m>f(2.5, 4.1, 4.8) \approx -1-0.04 = -1.04</m>.
+                  Using trigonometry, <m>\ell = x\tan(\theta)</m>,
+                  so <m>d\ell = \tan(\theta) dx + x\sec^2(\theta) d\theta</m>.
+                  With <m>\theta = 85^\circ</m> and <m>x=30</m>,
+                  we have <m>d\ell = 11.43dx+3949.38d\theta</m>.
+                  The measured length of the wall is much more sensitive to errors in <m>\theta</m> than in <m>x</m>.
+                  While it can be difficult to compare sensitivities between measuring feet and measuring degrees
+                  (it is somewhat like <q>comparing apples to oranges</q>),
+                  here the coefficients are so different that the result is clear:
+                  a small error in degree has a much greater impact than a small error in distance.
                 </p>
               </solution>
           <!--</webwork>-->
         </exercise>
 
-        <exercise label="ex-total-differential-approx-from-data-4">
-          <!--<webwork xml:id="webwork-ex-total-differential-approx-from-data-4">
+        <exercise label="ex-total-differential-error-analysis-4">
+          <!--<webwork xml:id="webwork-ex-total-differential-error-analysis-4">
               <pg-code>
               </pg-code>
               -->
               <statement>
                 <p>
-                  <m>f(3,3,3) = 5</m>,<nbsp/> <m>f_x(3,3,3) = 2</m>,<nbsp/>
-                  <m>f_y(3,3,3) = 0</m>,<nbsp/> <m>f_z(3,3,3) = -2</m>.
-                  Approximate <m>f(3.1, 3.1,3.1)</m>.
+                  It is <q>common sense</q> that it is far better to measure a long distance with a long measuring tape rather than a short one.
+                  A measured distance <m>D</m> can be viewed as the product of the length <m>\ell</m> of a measuring tape times the number <m>n</m> of times it was used.
+                  For instance,
+                  using a 3' tape 10 times gives a length of 30'. To measure the same distance with a 12' tape,
+                  we would use the tape 2.5 times. (<ie/>,
+                  <m>30=12\times 2.5</m>.) Thus <m>D = n\ell</m>.
                 </p>
-              </statement>
-              <solution>
+
                 <p>
-                  <m>dx = 0.1</m>, <m>dy = 0.1</m>, <m>dz = 0.1</m>.
+                  Suppose each time a measurement is taken with the tape,
+                  the recorded distance is within 1/16'' of the actual distance. (<ie/>, <m>d\ell = 1/16'' \approx 0.005</m>ft).
+                  Using differentials,
+                  show why common sense proves correct in that it is better to use a long tape to measure long distances.
                 </p>
-
+              </statement>
+              <solution>
                 <p>
-                  <m>dw = 2(0.1) + (0)(0.1) + (-2)(.1) = 0</m>,
-                  so <m>f(3.1,3.1,3.1) \approx 5+0=5</m>.
+                  With <m>D = n\ell</m>,
+                  the total differential is <m>dD = \ell\, dn+ n\,d\ell</m>.
+                  If one measures with a short tape,
+                  <m>n</m> must be large and hence
+                  <m>n\,d\ell</m> is going to be greater than when a large tape is used
+                  (wherein <m>n</m> will be small).
                 </p>
               </solution>
           <!--</webwork>-->
         </exercise>
-
       </exercisegroup>
     </subexercises>
   </exercises>
diff --git a/ptx/sec_trig_sub.ptx b/ptx/sec_trig_sub.ptx
index 37173eb05..52b842dbc 100644
--- a/ptx/sec_trig_sub.ptx
+++ b/ptx/sec_trig_sub.ptx
@@ -1337,8 +1337,6 @@
           </webwork>
         </exercise>
       </exercisegroup>
-
-      <enlarge-page skipsize="2"/>
       
       <exercisegroup cols="2" xml:id="exset-trig-sub-definite">
         <introduction>
diff --git a/ptx/sec_triple_int.ptx b/ptx/sec_triple_int.ptx
index 00c3a8ddd..56edeade2 100644
--- a/ptx/sec_triple_int.ptx
+++ b/ptx/sec_triple_int.ptx
@@ -2875,9 +2875,9 @@
       This leads us to a definition, followed by an example.
     </p>
 
-    <pagebreak-latex/>
+    <!-- <pagebreak-latex/> -->
     
-    <definition xml:id="def_triple_integral_2" hstretch="360">
+    <definition xml:id="def_triple_integral_2" hstretch="360" hskip="70">
       <title>Iterated Integration, (Part II)</title>
       <statement>
         <p>
@@ -3648,8 +3648,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            a domain <m>D</m> is described by its bounding surfaces,
+            A domain <m>D</m> is described by its bounding surfaces,
             along with a graph.
             Set up the triple integrals that give the volume of <m>D</m> in all 6 orders of integration,
             and find the volume of <m>D</m> by evaluating the indicated triple integral.
@@ -4783,7 +4782,7 @@
 
         <introduction>
           <p>
-            In the following exercises, evaluate the triple integral.
+            Evaluate the triple integral.
           </p>
         </introduction>
 
@@ -4857,8 +4856,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the center of mass of the solid represented by the indicated space region <m>D</m> with density function <m>\delta(x,y,z)</m>.
+            Find the center of mass of the solid represented by the indicated space region <m>D</m> with density function <m>\delta(x,y,z)</m>.
           </p>
         </introduction>
 
diff --git a/ptx/sec_vector_fields.ptx b/ptx/sec_vector_fields.ptx
index fe8c15882..2dece14eb 100644
--- a/ptx/sec_vector_fields.ptx
+++ b/ptx/sec_vector_fields.ptx
@@ -1781,8 +1781,7 @@
       <exercisegroup cols="2" xml:id="exset-vector-field-sketch">
         <introduction>
           <p>
-            In the following exercises,
-            sketch the given vector field over the rectangle with opposite corners <m>(-2,-2)</m> and <m>(2,2)</m>,
+            Sketch the given vector field over the rectangle with opposite corners <m>(-2,-2)</m> and <m>(2,2)</m>,
             sketching one vector for every point with integer coordinates (<ie/>, at <m>(0,0)</m>,
             <m>(1,2)</m>, etc.).
           </p>
@@ -2127,8 +2126,7 @@
       <exercisegroup cols="2" xml:id="ex-vector-field-div-curl">
         <introduction>
           <p>
-            In the following exercises,
-            find the divergence and curl of the given vector field.
+            Find the divergence and curl of the given vector field.
           </p>
         </introduction>
 
diff --git a/ptx/sec_vector_intro.ptx b/ptx/sec_vector_intro.ptx
index c1110180e..6d8469ef0 100644
--- a/ptx/sec_vector_intro.ptx
+++ b/ptx/sec_vector_intro.ptx
@@ -1085,7 +1085,7 @@
               This is sketched in <xref ref="fig_vect5"/>.
             </p>
 
-            <figure xml:id="fig_vect5" vshift="-2">
+            <figure xml:id="fig_vect5" vshift="1">
               <caption>Graphing vectors in <xref ref="ex_vect5"/>. All vectors shown have their initial point at the origin</caption>
             <!-- START figures/fig_vect5.tex -->
               <image width="47%">
@@ -1157,7 +1157,7 @@
     <em>parallel vectors</em>.
   </p>
 
-  <pagebreak-latex component="novideo"/>
+  <!-- <pagebreak-latex component="novideo"/> -->
   
   <definition xml:id="def_parallel_vectors">
     <title>Parallel Vectors</title>
@@ -1196,7 +1196,7 @@
     <m>\vec v_2</m> are parallel if there is a scalar <m>c\neq 0</m> such that <m>\vec v_1 = c\vec v_2</m>
     (see marginal note).
   </p>
-  <aside xml:id="aside-def-orthogonal" vshift="-1">
+  <aside xml:id="aside-def-orthogonal" vshift="-1.5">
     <title>Direction and the zero vector</title>
 
     <p>
@@ -1292,7 +1292,7 @@
         Find the force applied to each chain.
       </p>
 
-      <figure xml:id="fig_vect6" vshift="1">
+      <figure xml:id="fig_vect6" vshift="-1">
         <caption>A diagram of a weight hanging from 2 chains in <xref ref="ex_vect6"/></caption>
         <!-- START figures/fig_vect6.tex -->
         <image width="40%">
@@ -1542,7 +1542,7 @@
         How much higher will the weight be?
       </p>
 
-      <figure xml:id="fig_vect8" vshift="0">
+      <figure xml:id="fig_vect8" vshift="-2">
         <caption>A figure of a weight being pushed by the wind in <xref ref="ex_vect8"/></caption>
         <!-- START figures/fig_vect8.tex -->
         <image width="40%">
@@ -1788,7 +1788,7 @@
 
         <introduction>
           <p>
-            In the following exercises, points <m>P</m> and <m>Q</m> are given.
+            Points <m>P</m> and <m>Q</m> are given.
             Write the vector <m>\overrightarrow{PQ}</m> in component form and using the standard unit vectors.
           </p>
         </introduction>
@@ -2085,7 +2085,7 @@
 
         <introduction>
           <p>
-            In the following exercises, sketch <m>\vec u</m>, <m>\vec v</m>,
+            Sketch <m>\vec u</m>, <m>\vec v</m>,
             <m>\vec u+\vec v</m> and <m>\vec u-\vec v</m> on the same axes.
           </p>
         </introduction>
@@ -2468,7 +2468,7 @@
 
         <introduction>
           <p>
-            In the following exercises, find
+            Find
             <m>\norm{\vec u}</m>, <m>\norm{\vec v}</m>,
             <m>\norm{\vec u+\vec v}</m> and <m>\norm{\vec u-\vec v}</m>.
           </p>
@@ -2699,8 +2699,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the unit vector <m>\vec u</m> in the direction of <m>\vec v</m>.
+            Find the unit vector <m>\vec u</m> in the direction of <m>\vec v</m>.
           </p>
         </introduction>
 
@@ -2894,7 +2893,7 @@
             </image>
 
           <p>
-            In the following exercises, the angles <m>\theta</m> and <m>\varphi</m> are given.
+            Angles <m>\theta</m> and <m>\varphi</m> are given.
             Find the magnitude of the force applied to each chain.
           </p>
         </introduction>
@@ -3014,7 +3013,7 @@
             </image>
 
           <p>
-            In the following exercises, a force <m>\vec F_w</m> and length <m>\ell</m> are given.
+            A force <m>\vec F_w</m> and length <m>\ell</m> are given.
             Find the angle <m>\theta</m> and the height the weight is lifted as it moves to the right.
           </p>
         </introduction>
diff --git a/ptx/sec_vvf.ptx b/ptx/sec_vvf.ptx
index d9e01f08e..46ccae9c2 100644
--- a/ptx/sec_vvf.ptx
+++ b/ptx/sec_vvf.ptx
@@ -959,8 +959,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            sketch the vector-valued function on the given interval.
+            Sketch the vector-valued function on the given interval.
           </p>
         </introduction>
 
@@ -1348,8 +1347,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            sketch the vector-valued function on the given interval in <m>\mathbb{R}^3</m>.
+            Sketch the vector-valued function on the given interval in <m>\mathbb{R}^3</m>.
             Technology may be useful in creating the sketch.
           </p>
         </introduction>
@@ -1574,7 +1572,7 @@
 
         <introduction>
           <p>
-            In the following exercises, find <m>\norm{\vec r(t)}</m>.
+            Find <m>\norm{\vec r(t)}</m>.
           </p>
         </introduction>
 
diff --git a/ptx/sec_vvf_calc.ptx b/ptx/sec_vvf_calc.ptx
index 28390e083..f5aea28b6 100644
--- a/ptx/sec_vvf_calc.ptx
+++ b/ptx/sec_vvf_calc.ptx
@@ -2240,8 +2240,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            evaluate the given definite or indefinite integral.
+            Evaluate the given definite or indefinite integral.
           </p>
         </introduction>
 
diff --git a/ptx/sec_vvf_motion.ptx b/ptx/sec_vvf_motion.ptx
index 497d87e1a..4f219e34a 100644
--- a/ptx/sec_vvf_motion.ptx
+++ b/ptx/sec_vvf_motion.ptx
@@ -299,7 +299,7 @@
           the velocity of Object 2 is three times that of Object 1 and so it follows that the speed of Object 2 is three times that of Object 1 (<m>3\sqrt{5}</m> ft/s compared to <m>\sqrt{5}</m> ft/s.)
         </p>
 
-        <pagebreak-latex component="novideo"/>
+        <!-- <pagebreak-latex component="novideo"/> -->
 
         <figure xml:id="fig_motion2a" vshift="-2">
           <caption>Plotting velocity and acceleration vectors for Object 1 in <xref ref="ex_motion2"/></caption>
@@ -1407,7 +1407,7 @@
 
         <introduction>
           <p>
-            In the following exercises, a position function <m>\vrt</m> is given.
+            A position function <m>\vrt</m> is given.
             Find <m>\vvt</m> and <m>\vat</m>.
           </p>
         </introduction>
@@ -1515,7 +1515,7 @@
 
         <introduction>
           <p>
-            In the following exercises, a position function <m>\vrt</m> is given.
+            A position function <m>\vrt</m> is given.
             Sketch <m>\vrt</m> on the indicated interval.
             Find <m>\vvt</m> and <m>\vat</m>,
             then add <m>\vec v(t_0)</m> and <m>\vec a(t_0)</m> to your sketch,
@@ -1609,8 +1609,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            a position function <m>\vrt</m> of an object is given.
+            A position function <m>\vrt</m> of an object is given.
             Find the speed of the object in terms of <m>t</m>,
             and find where the speed is minimized/maximized on the indicated interval.
           </p>
@@ -1885,8 +1884,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            position functions <m>\vec r_1(t)</m> and
+            Position functions <m>\vec r_1(t)</m> and
             <m>\vec r_2(s)</m> for two objects are given that follow the same path on the respective intervals.
           </p>
 
@@ -2072,8 +2070,7 @@
 
         <introduction>
           <p>
-            In the following exercises,
-            find the position function of an object given its acceleration and initial velocity and position.
+            Find the position function of an object given its acceleration and initial velocity and position.
           </p>
         </introduction>
 
@@ -2164,7 +2161,7 @@
 
         <introduction>
           <p>
-            In the following exercises, find the displacement, distance traveled,
+            Find the displacement, distance traveled,
             average velocity and average speed of the described object on the given interval.
           </p>
         </introduction>
diff --git a/ptx/sec_work.ptx b/ptx/sec_work.ptx
index 374abe4ce..597785bcb 100644
--- a/ptx/sec_work.ptx
+++ b/ptx/sec_work.ptx
@@ -801,7 +801,7 @@
           note that the dimensions are for the water, not the pool itself.
           Compute the amount of work performed in draining the pool.
         </p>
-        <figure xml:id="fig_pump3" vshift="3">
+        <figure xml:id="fig_pump3" vshift="1">
           <caption>The cross-section of a swimming pool filled with water in <xref ref="ex_pump3"/></caption>
           <!-- START figures/fig_pump4.tex -->
           <image width="47%">
@@ -839,7 +839,7 @@
           meaning the top of the water is at <m>y=6</m>.
         </p>
 
-        <figure xml:id="fig_pump_3a" vshift="-1">
+        <figure xml:id="fig_pump_3a" vshift="-3">
           <caption>Orienting the pool and showing differential elements for <xref ref="ex_pump3"/></caption>
           <!-- START figures/fig_pump4b.tex -->
           <image width="47%">
diff --git a/publication/publication-color-print-novideo.ptx b/publication/publication-color-print-novideo.ptx
index 2706b4b31..85bc223d6 100644
--- a/publication/publication-color-print-novideo.ptx
+++ b/publication/publication-color-print-novideo.ptx
@@ -32,6 +32,16 @@
       <page>
         <geometry>inner=1in,textheight=9in,textwidth=320pt,marginparwidth=150pt,marginparsep=20pt,bottom=1in,footskip=29pt</geometry>
       </page>
+      <!-- page breaks in sections -->
+      <insertions pagebreaks="p-antider-break1 thm_deriv_glossary fig_disk0a fig_dotp3 fig_iterated6 fig_lines2 paragraphs-newton-convergence"/>
+      <insertions pagebreaks="fig_polar_roses subsec-series idea_shell_and_washer def_triple_integral_2 def_parallel_vectors fig_motion2a subsec-common-thread"/>
+      <insertions pagebreaks="riemann-summary-break subsec-polar-graphs thm_continuity_algebra def_infl thm_second_der thm_multi_second_test ex_iterated6"/>
+       <!-- page breaks in exercises. -->
+      <insertions pagebreaks="exset-deriv-implicit-tangent exset-definite-integral-area exset-definite-integral-velocity exset-definite-integral-properties"/>
+      <insertions pagebreaks="exset-riemann-integral-approx x07_01_ex_29 exset-alternating-series-bound-sum exset-conic-hyperbola-eqn-std"/>
+      <insertions pagebreaks="exset-parametric-describe-rectangular exset-vector-sum-sketch exset-limit-continuity-point exset-deriv-basic-higher"/>
+      <insertions pagebreaks="exset-trig-sub-definite exset-volume-shells-x-axis exset-power-series-find-series exset-cross-product-quadrilateral"/>
+      <insertions pagebreaks="exset-double-polar-special exset-cylindrical-spherical-setup exset-Greens-divergence"/>
     </latex>
     <epub>
       <cover front="cover/cover.png"/>
diff --git a/xsl/apex-latex-print-color.xsl b/xsl/apex-latex-print-color.xsl
index 83786fdfb..4110e787f 100644
--- a/xsl/apex-latex-print-color.xsl
+++ b/xsl/apex-latex-print-color.xsl
@@ -63,11 +63,11 @@
 </xsl:template>
 
 <xsl:template match="&DEFINITION-LIKE;" mode="tcb-style">
-    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, colbacktitle=yellow!90!black!30, colframe=yellow!95!black!60, colback=white!95!yellow, coltitle=black, titlerule=-0.3pt,</xsl:text>
+    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, before skip = \baselineskip, colbacktitle=yellow!90!black!30, colframe=yellow!95!black!60, colback=white!95!yellow, coltitle=black, titlerule=-0.3pt,</xsl:text>
 </xsl:template>
 
 <xsl:template match="&THEOREM-LIKE;" mode="tcb-style">
-    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, colbacktitle=green!60!black!20, colframe=green!30!black!50, colback=white!95!green, coltitle=black, titlerule=-0.3pt,</xsl:text>
+    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, before skip = \baselineskip, colbacktitle=green!60!black!20, colframe=green!30!black!50, colback=white!95!green, coltitle=black, titlerule=-0.3pt,</xsl:text>
 </xsl:template>
 
 <xsl:template match="assemblage" mode="tcb-style">
@@ -251,11 +251,12 @@ https://tex.stackexchange.com/questions/605955/can-i-avoid-indentation-of-margin
 </xsl:template>
 
 <!-- enable a few necessary page breaks to place images correctly -->
-<xsl:template match="pagebreak-latex">
+<!-- template is now obsolete: specify breaks in publisher file -->
+<!-- <xsl:template match="pagebreak-latex">
   <xsl:text>&#xa;</xsl:text>
   <xsl:text>\pagebreak</xsl:text>
   <xsl:text>&#xa;</xsl:text>
-</xsl:template>
+</xsl:template> -->
 
 <!-- and enable occasional enlarging of a page to avoid orphans -->
 <xsl:template match="enlarge-page">

From 26d83c16b28d3fb2b51acc8dd9a0d92b08534898 Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Thu, 4 Jun 2026 17:26:43 -0600
Subject: [PATCH 14/18] last? adjustments

---
 ptx/sec_cylindrical_spherical.ptx | 2 +-
 ptx/sec_iterated_integrals.ptx    | 2 +-
 ptx/sec_multi_extreme_values.ptx  | 4 ++--
 xsl/apex-latex-print-style.xsl    | 5 +++--
 xsl/apex-latex-style.xsl          | 5 +++--
 5 files changed, 10 insertions(+), 8 deletions(-)

diff --git a/ptx/sec_cylindrical_spherical.ptx b/ptx/sec_cylindrical_spherical.ptx
index 08a7319bb..8cac13c0d 100644
--- a/ptx/sec_cylindrical_spherical.ptx
+++ b/ptx/sec_cylindrical_spherical.ptx
@@ -927,7 +927,7 @@
       The following Key Idea gives conversions to/from our three spatial coordinate systems.
     </p>
 
-    <insight xml:id="idea_convert_coords" hstretch="330" hskip="60">
+    <insight xml:id="idea_convert_coords" hstretch="330" hskip="45">
     <!-- <insight xml:id="idea_convert_coords" hstretch="330"> -->
       <title>Converting Between Rectangular, Cylindrical and Spherical Coordinates</title>
       <p>
diff --git a/ptx/sec_iterated_integrals.ptx b/ptx/sec_iterated_integrals.ptx
index de21e4dc3..6c518e83d 100644
--- a/ptx/sec_iterated_integrals.ptx
+++ b/ptx/sec_iterated_integrals.ptx
@@ -461,7 +461,7 @@
           as shown in <xref ref="fig_iterated5"/>.
         </p>
 
-        <figure xml:id="fig_iterated5" vshift="0">
+        <figure xml:id="fig_iterated5" vshift="-2">
           <caption>Calculating the area of a triangle with iterated integrals in <xref ref="ex_iterated5"/></caption>
           <!-- START figures/fig_iterated5.tex -->
           <image width="47%">
diff --git a/ptx/sec_multi_extreme_values.ptx b/ptx/sec_multi_extreme_values.ptx
index 332757b63..3bc9e10b4 100644
--- a/ptx/sec_multi_extreme_values.ptx
+++ b/ptx/sec_multi_extreme_values.ptx
@@ -1078,7 +1078,7 @@
           We find <m>f(0,0) = 5</m>.
         </p>
 
-        <figure xml:id="fig_conopt1bX" vshift="0">
+        <figure xml:id="fig_conopt1bX" vshift="1">
           <caption>The graph of <m>f</m> along with important points along the boundary of <m>S</m> and the interior  in <xref ref="ex_conopt1"/></caption>
           <!-- START figures/figconopt1c_3D.asy -->
           <image width="47%">
@@ -1261,7 +1261,7 @@
           This gives a volume of <m>V(21.67,43.33) \approx 20,343</m>in<m>^3</m>.
         </p>
 
-        <figure xml:id="fig_conopt2" vshift="0">
+        <figure xml:id="fig_conopt2" vshift="2">
           <caption>Graphing the volume of a box with girth <m>4w</m> and length <m>\ell</m>, subject to a size constraint</caption>
 
           <!-- START figures/figconopt2_3D.asy -->
diff --git a/xsl/apex-latex-print-style.xsl b/xsl/apex-latex-print-style.xsl
index 98d595976..20f8181d2 100644
--- a/xsl/apex-latex-print-style.xsl
+++ b/xsl/apex-latex-print-style.xsl
@@ -251,11 +251,12 @@ https://tex.stackexchange.com/questions/605955/can-i-avoid-indentation-of-margin
 </xsl:template>
 
 <!-- enable a few necessary page breaks to place images correctly -->
-<xsl:template match="pagebreak-latex">
+<!-- template is now obsolete: specify breaks in publisher file -->
+<!-- <xsl:template match="pagebreak-latex">
   <xsl:text>&#xa;</xsl:text>
   <xsl:text>\pagebreak</xsl:text>
   <xsl:text>&#xa;</xsl:text>
-</xsl:template>
+</xsl:template> -->
 
 <!-- and enable occasional enlarging of a page to avoid orphans -->
 <xsl:template match="enlarge-page">
diff --git a/xsl/apex-latex-style.xsl b/xsl/apex-latex-style.xsl
index 4acd21f80..f52876be8 100644
--- a/xsl/apex-latex-style.xsl
+++ b/xsl/apex-latex-style.xsl
@@ -239,11 +239,12 @@ https://tex.stackexchange.com/questions/605955/can-i-avoid-indentation-of-margin
 </xsl:template>
 
 <!-- enable a few necessary page breaks to place images correctly -->
-<xsl:template match="pagebreak-latex">
+<!-- template is now obsolete: specify breaks in publisher file -->
+<!-- <xsl:template match="pagebreak-latex">
   <xsl:text>&#xa;</xsl:text>
   <xsl:text>\pagebreak</xsl:text>
   <xsl:text>&#xa;</xsl:text>
-</xsl:template>
+</xsl:template> -->
 
 <!-- and enable occasional enlarging of a page to avoid orphans -->
 <xsl:template match="enlarge-page">

From 51f44747abcb331dd0ac0881b4ee72d26249f7dc Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Thu, 4 Jun 2026 17:30:17 -0600
Subject: [PATCH 15/18] pubfile adjustments

---
 publication/publication-novid-print.ptx | 10 ++++++++++
 publication/publication-novid.ptx       |  2 +-
 2 files changed, 11 insertions(+), 1 deletion(-)

diff --git a/publication/publication-novid-print.ptx b/publication/publication-novid-print.ptx
index cafd3123d..33f3a70ab 100644
--- a/publication/publication-novid-print.ptx
+++ b/publication/publication-novid-print.ptx
@@ -30,6 +30,16 @@
       <page>
         <geometry>inner=1in,textheight=9in,textwidth=320pt,marginparwidth=150pt,marginparsep=20pt,bottom=1in,footskip=29pt</geometry>
       </page>
+      <!-- page breaks in sections -->
+      <insertions pagebreaks="p-antider-break1 thm_deriv_glossary fig_disk0a fig_dotp3 fig_iterated6 fig_lines2 paragraphs-newton-convergence"/>
+      <insertions pagebreaks="fig_polar_roses subsec-series idea_shell_and_washer def_triple_integral_2 def_parallel_vectors fig_motion2a subsec-common-thread"/>
+      <insertions pagebreaks="riemann-summary-break subsec-polar-graphs thm_continuity_algebra def_infl thm_second_der thm_multi_second_test ex_iterated6"/>
+       <!-- page breaks in exercises. -->
+      <insertions pagebreaks="exset-deriv-implicit-tangent exset-definite-integral-area exset-definite-integral-velocity exset-definite-integral-properties"/>
+      <insertions pagebreaks="exset-riemann-integral-approx x07_01_ex_29 exset-alternating-series-bound-sum exset-conic-hyperbola-eqn-std"/>
+      <insertions pagebreaks="exset-parametric-describe-rectangular exset-vector-sum-sketch exset-limit-continuity-point exset-deriv-basic-higher"/>
+      <insertions pagebreaks="exset-trig-sub-definite exset-volume-shells-x-axis exset-power-series-find-series exset-cross-product-quadrilateral"/>
+      <insertions pagebreaks="exset-double-polar-special exset-cylindrical-spherical-setup exset-Greens-divergence"/>
     </latex>
     <epub>
       <cover front="cover/cover.png"/>
diff --git a/publication/publication-novid.ptx b/publication/publication-novid.ptx
index 16f9de3e9..81f9cacda 100644
--- a/publication/publication-novid.ptx
+++ b/publication/publication-novid.ptx
@@ -5,7 +5,7 @@
     <!-- Relative path, relative to "main" source file -->
     <source>
         <directories external="../assets" generated="../generated-assets"/>
-        <version include="main color novideo taypoly-late"/>
+        <version include="main color novideo taypoly-late pdf"/>
     </source>
 
     <webwork server="https://webwork-dev.uleth.ca" course="apex-main"/>

From e2a3cd159fb27e92d6ed1328ff37a8d76c0427bf Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Thu, 4 Jun 2026 19:30:21 -0600
Subject: [PATCH 16/18] add space above theorem and definition in BW styles

---
 xsl/apex-latex-print-style.xsl | 4 ++--
 xsl/apex-latex-style.xsl       | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/xsl/apex-latex-print-style.xsl b/xsl/apex-latex-print-style.xsl
index 20f8181d2..4629b4060 100644
--- a/xsl/apex-latex-print-style.xsl
+++ b/xsl/apex-latex-print-style.xsl
@@ -63,11 +63,11 @@
 </xsl:template>
 
 <xsl:template match="&DEFINITION-LIKE;" mode="tcb-style">
-    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, colbacktitle=white, colframe=black, colback=white, coltitle=black, titlerule=-0.3pt,</xsl:text>
+    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, before skip = \baselineskip, colbacktitle=white, colframe=black, colback=white, coltitle=black, titlerule=-0.3pt,</xsl:text>
 </xsl:template>
 
 <xsl:template match="&THEOREM-LIKE;" mode="tcb-style">
-    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, colbacktitle=white, colframe=black, colback=white, coltitle=black, titlerule=-0.3pt,</xsl:text>
+    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, before skip = \baselineskip, colbacktitle=white, colframe=black, colback=white, coltitle=black, titlerule=-0.3pt,</xsl:text>
 </xsl:template>
 
 <xsl:template match="assemblage" mode="tcb-style">
diff --git a/xsl/apex-latex-style.xsl b/xsl/apex-latex-style.xsl
index f52876be8..d1b29ef22 100644
--- a/xsl/apex-latex-style.xsl
+++ b/xsl/apex-latex-style.xsl
@@ -63,11 +63,11 @@
 </xsl:template>
 
 <xsl:template match="&DEFINITION-LIKE;" mode="tcb-style">
-    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, colbacktitle=yellow!90!black!30, colframe=yellow!95!black!60, colback=white!95!yellow, coltitle=black, titlerule=-0.3pt,</xsl:text>
+    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, before skip = \baselineskip, colbacktitle=yellow!90!black!30, colframe=yellow!95!black!60, colback=white!95!yellow, coltitle=black, titlerule=-0.3pt,</xsl:text>
 </xsl:template>
 
 <xsl:template match="&THEOREM-LIKE;" mode="tcb-style">
-    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, colbacktitle=green!60!black!20, colframe=green!30!black!50, colback=white!95!green, coltitle=black, titlerule=-0.3pt,</xsl:text>
+    <xsl:text>before upper app={\setparstyle}, fonttitle=\normalfont\bfseries, before skip = \baselineskip, colbacktitle=green!60!black!20, colframe=green!30!black!50, colback=white!95!green, coltitle=black, titlerule=-0.3pt,</xsl:text>
 </xsl:template>
 
 <xsl:template match="assemblage" mode="tcb-style">

From e53273f7612404e92aeff63d7b1bc78d91e8cccf Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Fri, 5 Jun 2026 14:01:03 -0600
Subject: [PATCH 17/18] ajdustments for video version

---
 ptx/sec_FTC.ptx                               |  6 +-
 ptx/sec_Separable.ptx                         |  2 +-
 ptx/sec_arc_length.ptx                        |  6 +-
 ptx/sec_conic_sections.ptx                    | 10 +--
 ptx/sec_cylindrical_spherical.ptx             |  2 +-
 ptx/sec_def_int.ptx                           |  6 +-
 ptx/sec_deriv_basic_rules.ptx                 |  8 +--
 ptx/sec_deriv_chainrule.ptx                   |  2 +-
 ptx/sec_deriv_implicit.ptx                    |  8 +--
 ptx/sec_deriv_intro.ptx                       | 41 +++++++++++-
 ptx/sec_deriv_inverse_function.ptx            |  2 +-
 ptx/sec_deriv_prodquot.ptx                    |  4 +-
 ptx/sec_differentials.ptx                     |  9 +--
 ptx/sec_double_int_polar.ptx                  |  2 +-
 ptx/sec_double_int_volume.ptx                 |  8 +--
 ptx/sec_graph_concavity.ptx                   |  6 +-
 ptx/sec_graph_extreme_values.ptx              | 10 +--
 ptx/sec_graph_incr_decr.ptx                   |  6 +-
 ptx/sec_graph_mvt.ptx                         |  6 +-
 ptx/sec_improper_integration.ptx              | 12 ++--
 ptx/sec_lhopitals_rule.ptx                    |  2 +-
 ptx/sec_limit_analytically.ptx                |  6 +-
 ptx/sec_limit_continuity.ptx                  |  2 +-
 ptx/sec_limit_def.ptx                         |  4 +-
 ptx/sec_limit_infty.ptx                       |  6 +-
 ptx/sec_limit_intro.ptx                       | 28 ++++----
 ptx/sec_limit_onesided.ptx                    |  2 +-
 ptx/sec_lines.ptx                             |  4 +-
 ptx/sec_par_calc.ptx                          |  6 +-
 ptx/sec_param_eqs.ptx                         |  6 +-
 ptx/sec_partial_fraction.ptx                  | 20 +++---
 ptx/sec_planes.ptx                            |  6 +-
 ptx/sec_polar.ptx                             |  6 +-
 ptx/sec_polarcalc.ptx                         |  6 +-
 ptx/sec_ratio_root_tests.ptx                  |  2 +-
 ptx/sec_riemann.ptx                           |  2 +-
 ptx/sec_sequences.ptx                         |  4 +-
 ptx/sec_series.ptx                            |  2 +-
 ptx/sec_space_coord.ptx                       |  2 +-
 ptx/sec_stokes_divergence.ptx                 |  5 +-
 ptx/sec_tan_norm.ptx                          |  8 +--
 ptx/sec_taylor_poly.ptx                       | 64 ++++++++++++++++++-
 ptx/sec_transformations.ptx                   |  2 +-
 ptx/sec_trigint.ptx                           |  2 +-
 ptx/sec_vector_intro.ptx                      |  8 +--
 ptx/sec_vvf.ptx                               |  8 +--
 ptx/sec_vvf_calc.ptx                          |  2 +-
 ptx/sec_vvf_motion.ptx                        |  2 +-
 publication/publication-accelerated-print.ptx | 11 ++++
 publication/publication-accelerated.ptx       | 11 ++++
 .../publication-color-print-novideo.ptx       |  3 +-
 publication/publication-color-print.ptx       | 10 +++
 publication/publication-novid-print.ptx       |  3 +-
 publication/publication-novid.ptx             | 10 +++
 publication/publication-standard-print.ptx    | 11 ++++
 publication/publication-standard.ptx          | 11 ++++
 publication/publication.ptx                   | 11 ++++
 xsl/apex-latex-print-color.xsl                |  4 +-
 xsl/apex-latex-print-style.xsl                |  4 +-
 xsl/apex-latex-style.xsl                      |  4 +-
 60 files changed, 318 insertions(+), 148 deletions(-)

diff --git a/ptx/sec_FTC.ptx b/ptx/sec_FTC.ptx
index c36332121..a6899e262 100644
--- a/ptx/sec_FTC.ptx
+++ b/ptx/sec_FTC.ptx
@@ -1296,7 +1296,7 @@
           </md>
         </p>
       </solution>
-      <solution component="video" vshift="2">
+      <solution component="video" vshift="5">
         <title>Video solution</title>
         <video width="98%" youtube="su2CXdpYPdo" label="vid_int_FTC_ex_4" component="video"/>
       </solution>
@@ -1308,7 +1308,7 @@
       The video example in <xref ref="vid_int_FTC_ex_5"/> illustrates this phenomenon.
     </p>
 
-    <figure xml:id="vid_int_FTC_ex_5" component="video" vshift="-2">
+    <figure xml:id="vid_int_FTC_ex_5" component="video" vshift="2">
       <caption>Finding the area between curves that intersect multiple times</caption>
       <video youtube="Bgji1b7Wdr4" label="vid_int_FTC_ex_5"/>
     </figure>
@@ -1529,7 +1529,7 @@
       </statement>
     </theorem>
 
-    <figure xml:id="vid_int_FTC_MVT_int" component="video" vshift="0">
+    <figure xml:id="vid_int_FTC_MVT_int" component="video" vshift="5">
       <caption>Video presentation of <xref ref="thm_mvt2"/></caption>
       <video youtube="KD90CwK0PJk" label="vid_int_FTC_MVT_int"/>
     </figure>
diff --git a/ptx/sec_Separable.ptx b/ptx/sec_Separable.ptx
index 1214d24f0..67e936016 100644
--- a/ptx/sec_Separable.ptx
+++ b/ptx/sec_Separable.ptx
@@ -501,7 +501,7 @@
           The general solution the logistic differential equation is the set containing <m>\displaystyle y = \frac{M}{1 + be^{-kt}}</m> and <m>y=0</m>.
         </p>
       </solution>
-      <solution component="video" vshift="4">
+      <solution component="video" vshift="5">
         <title>Video solution</title>
         <video width="98%" youtube="nLItalqug6A" label="vid-diffeq-separable-example-logistic" component="video"/>
       </solution>
diff --git a/ptx/sec_arc_length.ptx b/ptx/sec_arc_length.ptx
index 0d1e2c200..1503025ee 100644
--- a/ptx/sec_arc_length.ptx
+++ b/ptx/sec_arc_length.ptx
@@ -366,7 +366,7 @@
           A graph of <m>f</m> is given in <xref ref="fig_arc1"/>.
         </p>
       </solution>
-      <solution component="video" vshift="5">
+      <solution component="video" vshift="-1">
         <title>Video solution</title>
         <video width="98%" youtube="0NPr4wZlTi8" label="vid-intapp-arclength-example1" component="video"/>
       </solution>
@@ -435,7 +435,7 @@
           the portion of the curve measured in this problem is in bold.
         </p>
       </solution>
-      <solution component="video" vshift="6">
+      <solution component="video" vshift="-1">
         <title>Video solution</title>
         <video width="98%" youtube="mJlyz_9yiao" label="vid-intapp-arclength-example2" component="video"/>
       </solution>
@@ -917,7 +917,7 @@
           involves both a square root and an inverse hyperbolic trigonometric function.
         </p>
       </solution>
-      <solution component="video" vshift="3">
+      <solution component="video" vshift="0">
         <title>Video solution</title>
         <video width="98%" youtube="ehC1adQ-pTs" label="vid-intapp-surfarea-example1" component="video"/>
       </solution>
diff --git a/ptx/sec_conic_sections.ptx b/ptx/sec_conic_sections.ptx
index f7b7a9992..e4670b6d2 100644
--- a/ptx/sec_conic_sections.ptx
+++ b/ptx/sec_conic_sections.ptx
@@ -381,7 +381,7 @@
           The parabola is sketched in <xref ref="fig_conic1"/>.
         </p>
       </solution>
-      <solution component="video" vshift="1">
+      <solution component="video" vshift="7">
         <title>Video solution</title>
         <video width="98%" youtube="dk8lrQac8Qg" label="vid-planecurves-conic-parabola-example1" component="video"/>
       </solution>
@@ -846,7 +846,7 @@
           </md>.
         </p>
       </solution>
-      <solution component="video" vshift="3">
+      <solution component="video" vshift="-3">
         <title>Video solution</title>
         <video width="98%" youtube="NVqlZCWDDnI" label="vid-planecurves-conic-ellipse-example1" component="video"/>
       </solution>
@@ -936,7 +936,7 @@
           <!-- figures/fig_conic4.tex END -->
         </figure>
       </solution>
-      <solution component="video" vshift="3">
+      <solution component="video" vshift="-3">
         <title>Video solution</title>
         <video width="98%" youtube="U3uhopYrG8o" label="vid-planecurves-conic-ellipse-example2" component="video"/>
       </solution>
@@ -1596,7 +1596,7 @@
             <m>(1,2\pm 5.4)</m> as shown in the figure.
           </p>
         </solution>
-        <solution component="video" vshift="5">
+        <solution component="video" vshift="6.5">
           <title>Video solution</title>
           <video width="98%" youtube="0YVNci7ZOfo" label="vid-planecurves-conic-hyperbola-example1" component="video"/>
         </solution>
@@ -1685,7 +1685,7 @@
             <m>(\pm 3.2,1)</m> as shown in the figure.
           </p>
         </solution>
-        <solution component="video" vshift="2">
+        <solution component="video" vshift="-2">
           <title>Video solution</title>
           <video width="98%" youtube="b-1_3ATvn9A" label="vid-planecurves-conic-hyperbola-example2" component="video"/>
         </solution>
diff --git a/ptx/sec_cylindrical_spherical.ptx b/ptx/sec_cylindrical_spherical.ptx
index 8cac13c0d..1ed8da025 100644
--- a/ptx/sec_cylindrical_spherical.ptx
+++ b/ptx/sec_cylindrical_spherical.ptx
@@ -914,7 +914,7 @@
       <video youtube="In5up-a1jMI" label="vid-multint-spherical-intro"/>
     </figure>
 
-    <aside xml:id="vidnote-aside-conventions" component="video" vshift="0">
+    <aside xml:id="vidnote-aside-conventions" component="video" vshift="-18">
       <p>
         The videos used in this section (and later) were recorded for an earlier version of the textbook,
         that used the polar angle instead of the elevation angle.
diff --git a/ptx/sec_def_int.ptx b/ptx/sec_def_int.ptx
index 5997a6508..e5d7d1f40 100644
--- a/ptx/sec_def_int.ptx
+++ b/ptx/sec_def_int.ptx
@@ -3,7 +3,7 @@
   <title>The Definite Integral</title>
 
 
-  <figure xml:id="vid_int_def_int_intro" component="video" vshift="0">
+  <figure xml:id="vid_int_def_int_intro" component="video" vshift="-18">
     <caption>Video introduction to <xref ref="sec_def_int"/></caption>
     <video youtube="__Xh37Qw4UE" label="vid_int_def_int_intro"/>
   </figure>
@@ -602,7 +602,7 @@
         </image>
       </figure>
     </solution>
-    <solution component="video" vshift="7">
+    <solution component="video" vshift="9">
       <title>Video solution</title>
       <video width="98%" youtube="jrjjVT1j9uw" label="vid_int_def_int_ex_1" component="video"/>
     </solution>
@@ -1064,7 +1064,7 @@
         hence its maximum displacement is 27 feet from its starting position.
       </p>
     </solution>
-    <solution component="video" vshift="0">
+    <solution component="video" vshift="-10">
       <title>Video solution</title>
       <video width="98%" youtube="2zJzbg0hNXE" label="vid_int_def_int_motion" component="video"/>
     </solution>
diff --git a/ptx/sec_deriv_basic_rules.ptx b/ptx/sec_deriv_basic_rules.ptx
index cf44179a1..bb0ca43ed 100644
--- a/ptx/sec_deriv_basic_rules.ptx
+++ b/ptx/sec_deriv_basic_rules.ptx
@@ -117,7 +117,7 @@
     
   </exercise>
 
-  <figure xml:id="vid_deriv_basic_rules" component="video" vshift="0">
+  <figure xml:id="vid_deriv_basic_rules" component="video" vshift="2.5">
     <caption>Video explanation of <xref ref="thm_deriv_common"/></caption>
     <video youtube="wPJ8-zKc1n0" label="vid_deriv_basic_rules"/>
   </figure>
@@ -287,7 +287,7 @@
         <!-- figures/fig_xcubedwithderiv.tex END -->
       </figure>
     </solution>
-    <solution component="video" vshift="5">
+    <solution component="video" vshift="8.5">
       <title>Video solution</title>
       <video width="98%" youtube="lyAEJSmSr-A" label="vid_deriv_basic_rules_ex" component="video"/>
     </solution>
@@ -394,7 +394,7 @@
     
   </exercise>
 
-  <figure xml:id="vid_deriv_basic_rules_const_sum_rule" component="video" vshift="2">
+  <figure xml:id="vid_deriv_basic_rules_const_sum_rule" component="video" vshift="1">
     <caption>Video presentation of <xref ref="thm_deriv_prop"/></caption>
     <video youtube="Hr0sQcVhQ9A" label="vid_deriv_basic_rules_const_sum_rule"/>
   </figure>
@@ -654,7 +654,7 @@
       </p>
     </aside>
 
-    <figure xml:id="vid_deriv_basic_rules_higher_order_deriv" component="video" vshift="0">
+    <figure xml:id="vid_deriv_basic_rules_higher_order_deriv" component="video" vshift="-1">
       <caption>Video explanation of <xref ref="def_Higher_Deriv"/></caption>
       <video youtube="usabSpUh65w" label="vid_deriv_basic_rules_higher_order_deriv"/>
     </figure>
diff --git a/ptx/sec_deriv_chainrule.ptx b/ptx/sec_deriv_chainrule.ptx
index 8265ac15b..f5aab8989 100644
--- a/ptx/sec_deriv_chainrule.ptx
+++ b/ptx/sec_deriv_chainrule.ptx
@@ -20,7 +20,7 @@
     <q>inside</q> another).
   </p>
 
-  <figure xml:id="vid_deriv_chain_intro" component="video" vshift="1">
+  <figure xml:id="vid_deriv_chain_intro" component="video" vshift="2">
     <caption>Video introduction to <xref ref="sec_chainrule"/></caption>
     <video youtube="k7wX-kxd7Kw" label="vid_deriv_chain_intro"/>
   </figure>
diff --git a/ptx/sec_deriv_implicit.ptx b/ptx/sec_deriv_implicit.ptx
index 252a9827c..c71385797 100644
--- a/ptx/sec_deriv_implicit.ptx
+++ b/ptx/sec_deriv_implicit.ptx
@@ -15,7 +15,7 @@
       Knowing <m>x</m>, we can directly find <m>y</m>.)
     </p>
 
-    <figure xml:id="vid_deriv_impl_intro" component="video" vshift="0">
+    <figure xml:id="vid_deriv_impl_intro" component="video" vshift="3">
       <caption>Video introduction to <xref ref="sec_imp_deriv"/></caption>
       <video youtube="E0mQbLG3Pjo" label="vid_deriv_impl_intro"/>
     </figure>
@@ -319,7 +319,7 @@
           <!-- figures/fig_implicit2.tex END -->
         </figure>
       </solution>
-      <solution component="video" vshift="6">
+      <solution component="video" vshift="8">
         <title>Video solution</title>
         <video width="98%" youtube="qYrcm4ObwOM" label="vid_deriv_impl_tan_line_prev_ex" component="video"/>
       </solution>
@@ -614,7 +614,7 @@
           <!-- figures/fig_implicit6.tex END -->
         </figure>
       </solution>
-      <solution component="video" vshift="6">
+      <solution component="video" vshift="8">
         <title>Video solution</title>
         <video width="98%" youtube="BMn-BU6VTQU" label="vid_deriv_impl_ex_3" component="video"/>
       </solution>
@@ -1086,7 +1086,7 @@
           <!-- figures/fig_implicit10.tex END -->
         </figure>
       </solution>
-      <solution component="video" vshift="2">
+      <solution component="video" vshift="-4">
         <title>Video solution</title>
         <video youtube="6eL6WBlmItk" label="vid_deriv_implicit_logarithmic1"/>
       </solution>
diff --git a/ptx/sec_deriv_intro.ptx b/ptx/sec_deriv_intro.ptx
index a3db3fd70..3b43609cb 100644
--- a/ptx/sec_deriv_intro.ptx
+++ b/ptx/sec_deriv_intro.ptx
@@ -579,7 +579,7 @@
       This is explained in the video in <xref ref="vid_deriv_intro_diff_imp_cont"/>.
     </p>
 
-    <figure xml:id="vid_deriv_intro_diff_imp_cont" component="video" vshift="-2">
+    <figure xml:id="vid_deriv_intro_diff_imp_cont" component="video" vshift="-4">
       <caption>Showing that every differentiable function is continuous</caption>
       <video youtube="Ev9hJVbDO1k" label="vid_deriv_intro_diff_imp_cont"/>
     </figure>
@@ -802,7 +802,44 @@
           The graph seems to imply the approximation is rather good.
         </p>
 
-        <figure xml:id="fig_tangentsinx" vshift="3">
+        <figure xml:id="fig_tangentsinx" vshift="3" component="novideo">
+          <caption><m>f(x) = \sin(x)</m> graphed with an approximation to its tangent line at <m>x=0</m></caption>
+          <!-- START figures/fig_tangentsinx.tex -->
+          <image width="47%">
+            <shortdescription>
+              A graph of function sin(x) with an approximation to its tangent line at x=0.
+            </shortdescription>
+            <description>
+              <p>
+                The <m>y</m> axis of the graph is drawn from <m>-1</m> to <m>1</m>
+                and the <m>x</m> axis is drawn from <m>-\pi</m> and <m>\pi</m>.
+                The sine graph has an <m>x</m> intercept at <m>-\pi</m> then enters the
+                third quadrant and forms an upward facing parabola
+                with its vertex at  point <m>(-\pi/2, -1)</m>.
+                It passes throgh the origin then enters the first quadrant forming a downward
+                facing parabola with vertex at <m>(\pi/2, 1)</m>.
+              </p>
+            </description>
+            <latex-image label="img_tangentsinx">
+              \begin{tikzpicture}
+                \begin{axis}[
+                    ymin=-1.1,
+                    ymax=1.1,
+                    xmin=-3.5,
+                    xmax=3.5,
+                    xtick={-3.14,-1.57,1.57,3.14},
+                    xticklabels={$-\pi$,$-\frac{\pi}2$,$\frac{\pi}2$,$\pi$}
+                  ]
+                  \addplot+[infinite,domain=-3.5:3.5,samples=101]{sin(deg(x))};
+                  \addplot+[tangentline,domain=-1:1] {sin(deg(1))*x};
+                  \addplot [soliddot] coordinates{(0,0)};
+                \end{axis}
+              \end{tikzpicture}
+            </latex-image>
+          </image>
+          <!-- figures/fig_tangentsinx.tex END -->
+        </figure>
+        <figure xml:id="fig_tangentsinx" vshift="-1" component="video">
           <caption><m>f(x) = \sin(x)</m> graphed with an approximation to its tangent line at <m>x=0</m></caption>
           <!-- START figures/fig_tangentsinx.tex -->
           <image width="47%">
diff --git a/ptx/sec_deriv_inverse_function.ptx b/ptx/sec_deriv_inverse_function.ptx
index f9bff723e..05726c4af 100644
--- a/ptx/sec_deriv_inverse_function.ptx
+++ b/ptx/sec_deriv_inverse_function.ptx
@@ -48,7 +48,7 @@
     then they are inverses.
   </p>
 
-  <figure xml:id="vid_deriv_inverse_prop" component="video" vshift="1">
+  <figure xml:id="vid_deriv_inverse_prop" component="video" vshift="-10">
     <caption>Properties of inverse functions</caption>
     <video youtube="1g9gAQC301Q" label="vid_deriv_inverse_prop"/>
   </figure>
diff --git a/ptx/sec_deriv_prodquot.ptx b/ptx/sec_deriv_prodquot.ptx
index b9cdeecab..ce7005067 100644
--- a/ptx/sec_deriv_prodquot.ptx
+++ b/ptx/sec_deriv_prodquot.ptx
@@ -120,7 +120,7 @@
           <!-- figures/fig_5xsquaredsinx.tex END -->
       </figure>
     </solution>
-    <solution component="video" vshift="4">
+    <solution component="video" vshift="9">
       <title>Video solution</title>
       <video width="98%" youtube="37efDywkDyE" label="vid_deriv_prod_quot_prod_ex" component="video"/>
     </solution>
@@ -545,7 +545,7 @@
         <!-- figures/fig_tanx.tex END -->
       </figure>
     </solution>
-    <solution component="video" vshift="6">
+    <solution component="video" vshift="9">
       <title>Video solution</title>
       <video width="98%" youtube="wslbADxDg4c" label="vid_deriv_prod_quot_tanx" component="video"/>
     </solution>
diff --git a/ptx/sec_differentials.ptx b/ptx/sec_differentials.ptx
index fd7007e02..0917f9507 100644
--- a/ptx/sec_differentials.ptx
+++ b/ptx/sec_differentials.ptx
@@ -398,13 +398,6 @@
     </p>
   </insight>
 
-  <p xml:id="vidint_deriv_apps_diff_dx_eq_delta_x" component="video">
-    When students first encounter differentials,
-    they are often left wondering why <m>dy</m> and <m>\Delta y</m> are different,
-    while <m>dx</m> and <m>\Delta x</m> are the same.
-    The video in <xref ref="vid_deriv_apps_diff_dx_eq_delta_x"/> attempts to offer an explanation.
-  </p>
-
   <figure xml:id="vid_deriv_apps_diff_dx_eq_delta_x" component="video" vshift="1">
     <caption>Why is it that <m>dx = \Delta x</m>?</caption>
     <video youtube="XxpcZw702nA" label="vid_deriv_apps_diff_dx_eq_delta_x"/>
@@ -558,7 +551,7 @@
         so we approximate <m>\sqrt{4.5} \approx 2.125</m>.
       </p>
     </solution>
-    <solution component="video" vshift="0">
+    <solution component="video" vshift="2">
       <title>Video solution</title>
       <video width="98%" youtube="nFaq1O_wWso" label="vid_deriv_apps_diff_ex_3" component="video"/>
     </solution>
diff --git a/ptx/sec_double_int_polar.ptx b/ptx/sec_double_int_polar.ptx
index 2936308d8..6d47f3cd9 100644
--- a/ptx/sec_double_int_polar.ptx
+++ b/ptx/sec_double_int_polar.ptx
@@ -381,7 +381,7 @@
         the volume is not very difficult to compute.
       </p>
 
-      <figure xml:id="fig_doublepol2" vshift="0">
+      <figure xml:id="fig_doublepol2">
         <caption>Showing the region <m>R</m> and surface used in <xref ref="ex_doublepol2"/></caption>
         <sidebyside widths="47% 47%" margins="0%">
           <figure xml:id="fig_doublepol2a">
diff --git a/ptx/sec_double_int_volume.ptx b/ptx/sec_double_int_volume.ptx
index d3be2e830..c8caa44ee 100644
--- a/ptx/sec_double_int_volume.ptx
+++ b/ptx/sec_double_int_volume.ptx
@@ -337,7 +337,7 @@
     This leads to a definition.
   </p>
 
-  <aside xml:id="note_doubleint" vshift="-2.5">
+  <aside xml:id="note_doubleint" vshift="-2">
     <title>Double integrals as limits of double sums</title>
 
     <p>
@@ -402,7 +402,7 @@
     </statement>
   </definition>
 
-  <figure xml:id="vid-multint-double-def" component="video" vshift="-5.5">
+  <figure xml:id="vid-multint-double-def" component="video" vshift="-5">
     <caption>Defining the double integral</caption>
     <video youtube="l7hGaXcsq9g" label="vid-multint-double-def"/>
   </figure>
@@ -884,7 +884,7 @@
     </solution>
   </example>
 
-  <figure xml:id="vid-multint-double-rectangle-eg" component="video" vshift="3.5">
+  <figure xml:id="vid-multint-double-rectangle-eg" component="video" vshift="3">
     <caption>Further examples of double integrals over rectangles</caption>
     <video youtube="MMbLzFw-5Rg" label="vid-multint-double-rectangle-eg"/>
   </figure>
@@ -1012,7 +1012,7 @@
     </statement>
   </theorem>
 
-  <figure xml:id="vid-multint-double-general-region" component="video" vshift="5">
+  <figure xml:id="vid-multint-double-general-region" component="video" vshift="11">
     <caption>Evaluating a double integral over a more general region</caption>
     <video youtube="FcxnuFSNOfY" label="vid-multint-double-general-region"/>
   </figure>
diff --git a/ptx/sec_graph_concavity.ptx b/ptx/sec_graph_concavity.ptx
index 3ec34877a..401d0464f 100644
--- a/ptx/sec_graph_concavity.ptx
+++ b/ptx/sec_graph_concavity.ptx
@@ -724,7 +724,7 @@
           <!-- figures/fig_conc1.tex END -->
         </figure>
       </solution>
-      <solution component="video" vshift="9">
+      <solution component="video" vshift="10.5">
         <title>Video solution</title>
         <video width="98%" youtube="n8TRVD_8sY0" label="vid_graphs_concav_ex_1" component="video"/>
       </solution>
@@ -1225,7 +1225,7 @@
       <!-- figures/fig_concavity6.tex END -->
     </figure>
 
-    <figure xml:id="vid_graphs_concav_second_deriv_test" component="video" vshift="-4">
+    <figure xml:id="vid_graphs_concav_second_deriv_test" component="video" vshift="-15">
       <caption>Video presentation of <xref ref="thm_second_der"/></caption>
       <video youtube="4hWldEUoG2U" label="vid_graphs_concav_second_deriv_test"/>
     </figure>
@@ -1296,7 +1296,7 @@
           <!-- figures/fig_conc4.tex END -->
         </figure>
       </solution>
-      <solution component="video" vshift="2">
+      <solution component="video" vshift="-6">
         <title>Video solution</title>
         <video width="98%" youtube="_DhmPXRZfi8" label="vid_graphs_concav_ex_4" component="video"/>
       </solution>
diff --git a/ptx/sec_graph_extreme_values.ptx b/ptx/sec_graph_extreme_values.ptx
index 228b3c10d..fcc38241e 100644
--- a/ptx/sec_graph_extreme_values.ptx
+++ b/ptx/sec_graph_extreme_values.ptx
@@ -51,7 +51,7 @@
     </statement>
   </definition>
 
-  <aside xml:id="aside-graph-extreme-terminology" vshift="2.5">
+  <aside xml:id="aside-graph-extreme-terminology" vshift="5">
     <p>
       <em>Note:</em> The extreme values of a function are
       <q><m>y</m></q> values,
@@ -65,7 +65,7 @@
     </p>
   </aside>
 
-  <figure xml:id="vid_graphs_extreme_val_abs_extrema" component="video" vshift="5">
+  <figure xml:id="vid_graphs_extreme_val_abs_extrema" component="video" vshift="0">
     <caption>Video presentation of <xref ref="def_extreme_values"/></caption>
     <video youtube="srE7xUmQtCQ" label="vid_graphs_extreme_val_abs_extrema"/>
   </figure>
@@ -217,7 +217,7 @@
     </statement>
   </theorem>
 
-  <figure xml:id="vid_graphs_extreme_val_EVT" component="video" vshift="2">
+  <figure xml:id="vid_graphs_extreme_val_EVT" component="video" vshift="7">
     <caption>Video presentation of <xref ref="thm_extreme_val"/></caption>
     <video youtube="GIcjxu8dTnY" label="vid_graphs_extreme_val_EVT"/>
   </figure>
@@ -315,7 +315,7 @@
     is a <m>y</m>-value that's the largest <m>y</m>-value <q>nearby.</q>
   </p>
 
-  <figure xml:id="vid_graphs_extreme_val_rel_extrema" component="video" vshift="-1">
+  <figure xml:id="vid_graphs_extreme_val_rel_extrema" component="video" vshift="10">
     <caption>Video presentation of <xref ref="def_rel_ext"/></caption>
     <video youtube="nBZTnxn0vqQ" label="vid_graphs_extreme_val_rel_extrema"/>
   </figure>
@@ -800,7 +800,7 @@
       </figure>
 
     </solution>
-    <solution component="video" vshift="0">
+    <solution component="video" vshift="-4.5">
       <title>Video solution</title>
       <video width="98%" youtube="LyhHlreZvhc" label="vid_graphs_extreme_val_ex_1" component="video"/>
     </solution>
diff --git a/ptx/sec_graph_incr_decr.ptx b/ptx/sec_graph_incr_decr.ptx
index d11069430..e2097fd2d 100644
--- a/ptx/sec_graph_incr_decr.ptx
+++ b/ptx/sec_graph_incr_decr.ptx
@@ -159,7 +159,7 @@
     </cardsort>
   </exercise>
 
-  <figure xml:id="vid_graphs_incr_decr_defn" component="video" vshift="0">
+  <figure xml:id="vid_graphs_incr_decr_defn" component="video" vshift="-10">
     <caption>Video presentation of <xref ref="def_incr_decr"/></caption>
     <video youtube="NtV0R-JxrmM" label="vid_graphs_incr_decr_defn"/>
   </figure>
@@ -622,7 +622,7 @@
         <!-- figures/fig_incr1.tex END -->
       </figure>
     </solution>
-    <solution component="video" vshift="10">
+    <solution component="video" vshift="16">
       <title>Video solution</title>
       <video width="98%" youtube="DW6qcgE1TZ0" label="vid_graphs_incr_decr_ex_1" component="video"/>
     </solution>
@@ -1251,7 +1251,7 @@
         <!-- figures/fig_incr3.tex END -->
       </figure>
     </solution>
-    <solution component="video" vshift="3">
+    <solution component="video" vshift="7">
       <title>Video solution</title>
       <video width="98%" youtube="T4RxcQnNotc" label="vid_graphs_incr_decr_ex_3" component="video"/>
     </solution>
diff --git a/ptx/sec_graph_mvt.ptx b/ptx/sec_graph_mvt.ptx
index 5ecec4303..998eebbc6 100644
--- a/ptx/sec_graph_mvt.ptx
+++ b/ptx/sec_graph_mvt.ptx
@@ -251,7 +251,7 @@
     </statement>
   </theorem>
 
-  <figure xml:id="vid_graphs_MVT_rolles_thm" component="video" vshift="8">
+  <figure xml:id="vid_graphs_MVT_rolles_thm" component="video" vshift="9">
     <caption>Video presentation of <xref ref="thm_rolles"/></caption>
     <video youtube="E05H1f8TByI" label="vid_graphs_MVT_rolles_thm"/>
   </figure>
@@ -308,7 +308,7 @@
     The video in <xref ref="vid_graphs_MVT_ex_1"/> illustrates one such use of Rolle's Theorem.
   </p>
 
-  <figure xml:id="vid_graphs_MVT_ex_1" component="video" vshift="-1">
+  <figure xml:id="vid_graphs_MVT_ex_1" component="video" vshift="8">
     <caption>Using Rolle's Theorem to show a polynomial has at most one real root</caption>
     <video youtube="le-5zsb6O7o" label="vid_graphs_MVT_ex_1"/>
   </figure>
@@ -496,7 +496,7 @@
           <!-- figures/fig_mvt4.tex END -->
       </figure>
     </solution>
-    <solution component="video" vshift="6">
+    <solution component="video" vshift="8">
       <title>Video solution</title>
       <video width="98%" youtube="ON7WYLJY2tE" label="vid_graphs_MVT_ex_3" component="video"/>
     </solution>
diff --git a/ptx/sec_improper_integration.ptx b/ptx/sec_improper_integration.ptx
index 664dd1070..59559de89 100644
--- a/ptx/sec_improper_integration.ptx
+++ b/ptx/sec_improper_integration.ptx
@@ -81,7 +81,7 @@
       <!-- figures/fig_improper1.tex END -->
     </figure>
 
-    <figure xml:id="vid-int-improper-intro" component="video" vshift="6">
+    <figure xml:id="vid-int-improper-intro" component="video" vshift="9">
       <caption>Video introduction to <xref ref="sec_improper_integration"/></caption>
       <video youtube="HhBRqV7rt4I" label="vid-int-improper-intro"/>
     </figure>
@@ -431,7 +431,7 @@
           </ol>
         </p>
       </solution>
-      <solution component="video" vshift="7">
+      <solution component="video" vshift="8.5">
         <title>Video solution</title>
         <video width="98%" youtube="hXnmu7fZj-E" label="vid-int-improper-ex-at-infinity" component="video"/>
       </solution>
@@ -719,7 +719,7 @@
           </ol>
         </p>
       </solution>
-      <solution component="video" vshift="1">
+      <solution component="video" vshift="-2">
         <title>Video solution</title>
         <video width="98%" youtube="F46oIXOBjAw" label="vid-int-improper-ex-vert-asy" component="video"/>
       </solution>
@@ -1062,7 +1062,7 @@
           </ol>
         </p>
       </solution>
-      <solution component="video" vshift="5">
+      <solution component="video" vshift="-1">
         <title>Video solution</title>
         <video width="98%" youtube="356-QIN7fWA" label="vid-int-improper-ex-compare-direct" component="video"/>
       </solution>
@@ -1203,7 +1203,7 @@
           <!-- figures/fig_impint6.tex END -->
         </figure>
       </solution>
-      <solution component="video" vshift="6">
+      <solution component="video" vshift="-2">
         <title>Video solution</title>
         <video width="98%" youtube="nIr1A1Tmako" label="vid-int-improper-ex-limit-compare" component="video"/>
       </solution>
@@ -1243,7 +1243,7 @@
       they are omitted from this text.
     </p>
 
-    <aside vshift="-2">
+    <aside vshift="-5">
       <p>
         If you do need to use comparison for an improper integral with infinite range,
         it is generally wise to stick with direct comparison.
diff --git a/ptx/sec_lhopitals_rule.ptx b/ptx/sec_lhopitals_rule.ptx
index 0120f06cc..b9a8bc2c2 100644
--- a/ptx/sec_lhopitals_rule.ptx
+++ b/ptx/sec_lhopitals_rule.ptx
@@ -556,7 +556,7 @@
           </ol>
         </p>
       </solution>
-      <solution component="video" vshift="7">
+      <solution component="video" vshift="8">
         <title>Video solution</title>
         <video width="98%" youtube="wHCd7Wsxzug" label="vid-lhospital-ex-expforms" component="video"/>
       </solution>
diff --git a/ptx/sec_limit_analytically.ptx b/ptx/sec_limit_analytically.ptx
index 03d67c50a..fb6f3eaa0 100644
--- a/ptx/sec_limit_analytically.ptx
+++ b/ptx/sec_limit_analytically.ptx
@@ -616,7 +616,7 @@
     </image>
   </figure>
 
-  <figure xml:id="vid_limit_analytic_squeeze_thm" component="video" vshift="-2">
+  <figure xml:id="vid_limit_analytic_squeeze_thm" component="video" vshift="7">
     <caption>Explaining the Squeeze Theorem</caption>
     <video youtube="8Tv-GRQdAVA" label="vid_limit_analytic_squeeze_thm"/>
   </figure>
@@ -633,7 +633,7 @@
     can be done by direct substitution, as the videos in <xref ref="vid_limit_analytic_lim_sin_0"/> illustrate.
   </p>
 
-  <figure xml:id="vid_limit_analytic_lim_sin_0" component="video" vshift="-5.5">
+  <figure xml:id="vid_limit_analytic_lim_sin_0" component="video" vshift="-2">
     <caption>Using the Squeeze Theorem to take the limit of <m>\sin(x)</m> at <m>0</m></caption>
     <video youtube="2pVHlrPee2w" label="vid_limit_analytic_lim_sin_0"/>
   </figure>
@@ -1191,7 +1191,7 @@
         </md>.
       </p>
     </solution>
-    <solution component="video" vshift="3">
+    <solution component="video" vshift="0">
       <title>Video solution</title>
       <video width="98%" youtube="MSckoYqdKH4" label="vid_limit_analytic_alg_ex_1" component="video"/>
     </solution>
diff --git a/ptx/sec_limit_continuity.ptx b/ptx/sec_limit_continuity.ptx
index 15d835226..3d091ed6a 100644
--- a/ptx/sec_limit_continuity.ptx
+++ b/ptx/sec_limit_continuity.ptx
@@ -759,7 +759,7 @@
     the above theorems allow us to quickly construct new continuous functions from old ones.
   </p>
 
-  <figure xml:id="vid_limit_con_using_prop" component="video" vshift="-1.5">
+  <figure xml:id="vid_limit_con_using_prop" component="video" vshift="0">
     <caption>Continuity of compositions</caption>
     <video youtube="ewUiuE9bQlo" label="vid_limit_con_using_prop"/>
   </figure>
diff --git a/ptx/sec_limit_def.ptx b/ptx/sec_limit_def.ptx
index faafa93ae..a3c62472c 100644
--- a/ptx/sec_limit_def.ptx
+++ b/ptx/sec_limit_def.ptx
@@ -190,7 +190,7 @@
     
   </exercise>
 
-  <figure xml:id="vid_limit_defn_precise" component="video" vshift="-2">
+  <figure xml:id="vid_limit_defn_precise" component="video" vshift="2">
     <caption>Video presentation of <xref ref="def_limit"/></caption>
     <video youtube="npoSY-AFvOY" label="vid_limit_defn_precise"/>
   </figure>
@@ -464,7 +464,7 @@
         that <m>\lim_{x\to 4} \sqrt{x} = 2</m>.
       </p>
     </solution>
-    <solution component="video" vshift="3">
+    <solution component="video" vshift="5">
       <title>Video solution</title>
       <video width="98%" youtube="qHWI0eha_rA" label="vid_limit_defn_sqrt_epsilon" component="video"/>
     </solution>
diff --git a/ptx/sec_limit_infty.ptx b/ptx/sec_limit_infty.ptx
index 5fad14596..3788cbebf 100644
--- a/ptx/sec_limit_infty.ptx
+++ b/ptx/sec_limit_infty.ptx
@@ -284,7 +284,7 @@
           So we may say <m>\lim_{x\to 1}1/{(x-1)^2}=\infty</m>.
         </p>
       </solution>
-      <solution component="video" vshift="8">
+      <solution component="video" vshift="12">
         <title>Video solution</title>
         <video width="98%" youtube="S3dUAUQiKFQ" label="vid_limit_inf_ex_using_defn" component="video"/>
       </solution>
@@ -492,7 +492,7 @@
           <!-- figures/fig_multipleasymptotes.tex END -->
         </figure>
       </solution>
-      <solution component="video" vshift="1.5">
+      <solution component="video" vshift="-2">
         <title>Video solution</title>
         <video width="98%" youtube="h-1BCF_lsHI" label="vid_limit_inf_vert_asymptotes_ex" component="video"/>
       </solution>
@@ -520,7 +520,7 @@
       rather, a hole exists in the graph at <m>x=1</m>.
     </p>
 
-    <figure xml:id="fig_noasy" vshift="1">
+    <figure xml:id="fig_noasy" vshift="-2">
       <caption>Graphically showing that <m>f(x) = \frac{x^2-1}{x-1}</m> does not have an asymptote at <m>x=1</m></caption>
       <!-- START figures/fig_noasy.tex -->
       <image width="47%">
diff --git a/ptx/sec_limit_intro.ptx b/ptx/sec_limit_intro.ptx
index 7e5b10c66..5dc8ba9da 100644
--- a/ptx/sec_limit_intro.ptx
+++ b/ptx/sec_limit_intro.ptx
@@ -209,7 +209,7 @@
     since we are working with the pseudo-definition of a limit,
     not the actual definition.)
   </p>
-  <figure xml:id="vid_limit_intro_sinxoverx" component="video" vshift="0">
+  <figure xml:id="vid_limit_intro_sinxoverx" component="video" vshift="0.25">
     <caption>Investigating <m>\sin(x)/x</m></caption>
     <video youtube="__qzaSg4y1I" label="vid_limit_intro_sinxoverx"/>
   </figure>
@@ -648,11 +648,6 @@
 
   <paragraphs xml:id="subsec_nolimit3">
     <title>Identifying When Limits Do Not Exist</title>
-    <figure xml:id="vid_limit_intro_limit_dne" component="video" vshift="-2">
-      <caption>Discussing ways in which a limit can fail to exist</caption>
-      <video youtube="DSIaDa_ABxo" label="vid_limit_intro_limit_dne"/>
-    </figure>
-
     <p>
       A function may not have a limit for all values of <m>x</m>.
       That is, we cannot write that <m>\lim_{x\to c}f(x)=L</m>
@@ -685,6 +680,11 @@
       We'll explore each of these in turn.
     </p>
 
+    <figure xml:id="vid_limit_intro_limit_dne" component="video" vshift="1">
+      <caption>Discussing ways in which a limit can fail to exist</caption>
+      <video youtube="DSIaDa_ABxo" label="vid_limit_intro_limit_dne"/>
+    </figure>
+
     <example xml:id="ex_no_limit1">
       <title>Different Values Approached From Left and Right</title>
       <statement>
@@ -800,6 +800,11 @@
       </solution>
     </example>
 
+    <figure xml:id="vid_limit_intro_jumps_asymptotes" component="video" vshift="0">
+      <caption>Video presentation for <xref first="ex_no_limit1" last="ex_no_limit2">Examples</xref></caption>
+      <video youtube="NnV1A1KTbg0" label="vid_limit_intro_jumps_asymptotes"/>
+    </figure>
+
     <example xml:id="ex_no_limit2">
       <title>The Function Grows Without Bound</title>
       <statement>
@@ -902,11 +907,6 @@
       </solution>
     </example>
 
-    <figure xml:id="vid_limit_intro_jumps_asymptotes" component="video" vshift="0">
-      <caption>Video presentation for <xref first="ex_no_limit1" last="ex_no_limit2">Examples</xref></caption>
-      <video youtube="NnV1A1KTbg0" label="vid_limit_intro_jumps_asymptotes"/>
-    </figure>
-
     <example xml:id="ex_no_limit3">
       <title>The Function Oscillates</title>
       <statement>
@@ -1139,7 +1139,7 @@
           <m>\lim_{x\to 0}\sin(1/x)</m> does not exist.
         </p>
       </solution>
-      <solution component="video" vshift="6">
+      <solution component="video" vshift="10">
         <title>Video solution</title>
         <video width="98%" youtube="gGvvFX5QyjE" label="vid_limit_intro_limit_oscillation" component="video"/>
       </solution>
@@ -1190,7 +1190,7 @@
           <idx><h>limit</h><h>difference quotient</h></idx>
 
     </p>
-    <figure xml:id="vid_limit_intro_limit_diff_quot" component="video" vshift="-3">
+    <figure xml:id="vid_limit_intro_limit_diff_quot" component="video" vshift="0">
       <caption>Introducing the difference quotient</caption>
       <video youtube="2NJmd0Jrt4U" label="vid_limit_intro_limit_diff_quot"/>
     </figure>
@@ -1466,7 +1466,7 @@
         </row>
       </tabular>
     </figure>
-    <figure xml:id="vid_limit_intro_limit_diff_quot_ex" component="video" vshift="-2">
+    <figure xml:id="vid_limit_intro_limit_diff_quot_ex" component="video" vshift="-3">
       <caption>Video examples for difference quotients: once with direct computation, and then by simplifying first</caption>
       <video youtube="YplEX5ohJk0" label="vid_limit_intro_limit_diff_quot_ex"/>
     </figure>
diff --git a/ptx/sec_limit_onesided.ptx b/ptx/sec_limit_onesided.ptx
index 2f794a779..d1f0980a5 100644
--- a/ptx/sec_limit_onesided.ptx
+++ b/ptx/sec_limit_onesided.ptx
@@ -741,7 +741,7 @@
         It is also clearly stated that <m>f(1) = 1</m>.
       </p>
     </solution>
-    <solution component="video" vshift="0.5">
+    <solution component="video" vshift="-1.5">
       <title>Video solution</title>
       <video width="98%" youtube="HVFazve-Qxc" label="vid_limit_one_sided_ex_4" component="video"/>
     </solution>
diff --git a/ptx/sec_lines.ptx b/ptx/sec_lines.ptx
index 5f11d533a..de47c395a 100644
--- a/ptx/sec_lines.ptx
+++ b/ptx/sec_lines.ptx
@@ -706,7 +706,7 @@
           Therefore, we conclude that the lines <m>\ell_1</m> and <m>\ell_2</m> are skew.
         </p>
       </solution>
-      <solution component="video" vshift="1">
+      <solution component="video" vshift="-1">
         <title>Video solution</title>
         <video width="98%" youtube="hEYfincwMX0" label="vid-vectors-lines-compare" component="video"/>
       </solution>
@@ -939,7 +939,7 @@
       </md>.
     </p>
 
-    <figure xml:id="vid-vectors-lines-distance-point" component="video" vshift="0">
+    <figure xml:id="vid-vectors-lines-distance-point" component="video" vshift="-1">
       <caption>Determining distance from a line to a point</caption>
       <video youtube="ZJ_e_0s2s2M" label="vid-vectors-lines-distance-point"/>
     </figure>
diff --git a/ptx/sec_par_calc.ptx b/ptx/sec_par_calc.ptx
index e080451ee..8461bdf54 100644
--- a/ptx/sec_par_calc.ptx
+++ b/ptx/sec_par_calc.ptx
@@ -500,7 +500,7 @@
           therefore the tangent line is <m>y=0</m>, the <m>x</m>-axis.
         </p>
       </solution>
-      <solution component="video" vshift="5">
+      <solution component="video" vshift="0">
         <title>Video solution</title>
         <video width="98%" youtube="rb4wEkhcUtE" label="vid-planecurves-parcalc-astroid" component="video"/>
       </solution>
@@ -1108,10 +1108,10 @@
           Increasing <m>n</m> shows that this value is stable and a good approximation of the actual value.
         </p>
       </solution>
-      <solution component="video" vshift="0">
+      <!-- <solution component="video" vshift="2">
         <title>Video solution</title>
         <video width="98%" youtube="G5U9BVhB3PE" label="vid-planecurves-parcalc-arclength-example2" component="video"/>
-      </solution>
+      </solution> -->
     </example>
 
     <exercise label="APEX-PROTEUS-par-calc-3-v1" component="proteus">
diff --git a/ptx/sec_param_eqs.ptx b/ptx/sec_param_eqs.ptx
index a4f211604..8074f793f 100644
--- a/ptx/sec_param_eqs.ptx
+++ b/ptx/sec_param_eqs.ptx
@@ -1038,7 +1038,7 @@
           the graph defined by <m>y=1-x</m> with unrestricted domain is given in a thin line.
         </p>
       </solution>
-      <solution component="video" vshift="0">
+      <solution component="video" vshift="4">
         <title>Video solution</title>
         <video width="98%" youtube="8Vgv74zCWFQ" label="vid-planecurves-parameq-elim-param" component="video"/>
       </solution>
@@ -1110,7 +1110,7 @@
           demonstrating that the graph is indeed of an ellipse with a horizontal major axis and center at <m>(3,1)</m>.
         </p>
       </solution>
-      <solution component="video" vshift="3">
+      <solution component="video" vshift="8">
         <title>Video solution</title>
         <video width="98%" youtube="RYkPHhpgnas" label="vid-planecurves-parameq-ellipse" component="video"/>
       </solution>
@@ -1576,7 +1576,7 @@
           <!-- figures/fig_pareq9.tex END -->
         </figure>
       </solution>
-      <solution component="video" vshift="3">
+      <solution component="video" vshift="6">
         <title>Video solution</title>
         <video width="98%" youtube="rqhh0McArDM" label="vid-planecurves-parameq-nonsmooth" component="video"/>
       </solution>
diff --git a/ptx/sec_partial_fraction.ptx b/ptx/sec_partial_fraction.ptx
index ad58d32f6..08d6d20a5 100644
--- a/ptx/sec_partial_fraction.ptx
+++ b/ptx/sec_partial_fraction.ptx
@@ -86,15 +86,17 @@
         </li>
       </ol>
     </p>
-<aside vshift="2">
-    <p>
-      An irreducible quadratic is a quadratic that has no real solutions.
-      Solving <m>ax^2+bx+c=0</m> using the quadratic equation will determine if a quadratic is irreducible.
-      Completing the square
-      (which is a common integration technique)
-      will also tell you if a quadratic is irreducible.
-    </p>
-  </aside>
+
+    <aside vshift="2">
+      <p>
+        An irreducible quadratic is a quadratic that has no real solutions.
+        Solving <m>ax^2+bx+c=0</m> using the quadratic equation will determine if a quadratic is irreducible.
+        Completing the square
+        (which is a common integration technique)
+        will also tell you if a quadratic is irreducible.
+      </p>
+    </aside>
+
     <p>
       To find the coefficients <m>A_i</m>,
       <m>B_i</m> and <m>C_i</m>:
diff --git a/ptx/sec_planes.ptx b/ptx/sec_planes.ptx
index a7d1e2a54..82578d290 100644
--- a/ptx/sec_planes.ptx
+++ b/ptx/sec_planes.ptx
@@ -301,7 +301,7 @@
           <!-- figures/figplanes1_3D.asy END -->
         </figure>
       </solution>
-      <solution component="video" vshift="3">
+      <solution component="video" vshift="6">
         <title>Video solution</title>
         <video width="98%" youtube="oc77R0am1vk" label="vid-vectors-planes-3points" component="video"/>
       </solution>
@@ -530,7 +530,7 @@
           <!-- figures/figplanes3_3D.asy END -->
         </figure>
       </solution>
-      <solution component="video" vshift="3">
+      <solution component="video" vshift="4">
         <title>Video solution</title>
         <video width="98%" youtube="2diP-H-QLoI" label="vid-vectors-planes-given-normal" component="video"/>
       </solution>
@@ -795,7 +795,7 @@
           <!-- figures/figplanes5_3D.asy END -->
         </figure>
       </solution>
-      <solution component="video" vshift="5">
+      <solution component="video" vshift="6">
         <title>Video solution</title>
         <video width="98%" youtube="DjuaixH0ayo" label="vid-vectors-planes-lineint" component="video"/>
       </solution>
diff --git a/ptx/sec_polar.ptx b/ptx/sec_polar.ptx
index affb0ac54..9c6e8f454 100644
--- a/ptx/sec_polar.ptx
+++ b/ptx/sec_polar.ptx
@@ -783,7 +783,7 @@
         </figure>
 
       </solution>
-      <solution component="video" vshift="5">
+      <solution component="video" vshift="7">
         <title>Video solution</title>
         <video width="98%" youtube="1omaozpN7wI" label="vid-planecurves-polar-cardioid" component="video"/>
       </solution>
@@ -2008,7 +2008,7 @@
         </figure>
 
         <p>
-          We start by setting the two functions equal to each other and solving for <m>\theta</m>:
+          To start we set the functions equal to each other and solve for <m>\theta</m>:
           <md>
             <mrow>1+3\cos(\theta) \amp = \cos(\theta)</mrow>
             <mrow>2\cos(\theta) \amp = -1</mrow>
@@ -2019,7 +2019,7 @@
 
         <p>
           (There are, of course,
-          infinite solutions to the equation <m>\cos(\theta) =-1/2</m>;
+          infinitely many solutions to the equation <m>\cos(\theta) =-1/2</m>;
           as the limaçon is traced out once on <m>[0,2\pi]</m>,
           we restrict our solutions to this interval.)
         </p>
diff --git a/ptx/sec_polarcalc.ptx b/ptx/sec_polarcalc.ptx
index f90576c71..0b996a578 100644
--- a/ptx/sec_polarcalc.ptx
+++ b/ptx/sec_polarcalc.ptx
@@ -332,7 +332,7 @@
           <!-- figures/fig_polcalc2.tex END -->
         </figure>
       </solution>
-      <solution component="video" vshift="5">
+      <solution component="video" vshift="7">
         <title>Video solution</title>
         <video width="98%" youtube="1bAf6kE9F1Y" label="vid-planecurves-polarcalc-polar-tangent" component="video"/>
       </solution>
@@ -601,7 +601,7 @@
           We did this example to demonstrate that the area formula is correct.
         </p>
       </solution>
-      <solution component="video" vshift="0">
+      <solution component="video" vshift="-2">
         <title>Video solution</title>
         <video width="98%" youtube="T_z8FNS3Whs" label="vid-planecurves-polarcalc-example-area1" component="video"/>
       </solution>
@@ -1169,7 +1169,7 @@
           which is accurate to 4 places after the decimal.)
         </p>
       </solution>
-      <solution component="video" vshift="4">
+      <solution component="video" vshift="7">
         <title>Video solution</title>
         <video width="98%" youtube="o-cetriP4Ms" label="vid-planecurves-polarcalc-arclength" component="video"/>
       </solution>
diff --git a/ptx/sec_ratio_root_tests.ptx b/ptx/sec_ratio_root_tests.ptx
index 449d031f3..4c542b3a4 100644
--- a/ptx/sec_ratio_root_tests.ptx
+++ b/ptx/sec_ratio_root_tests.ptx
@@ -308,7 +308,7 @@
       </statement>
     </theorem>
 
-    <figure xml:id="vid-seqseries-ratroot-root-test" component="video" vshift="3">
+    <figure xml:id="vid-seqseries-ratroot-root-test" component="video" vshift="-1">
       <caption>Video presentation of <xref ref="thm_root_test"/></caption>
       <video youtube="foE1iRYTXpc" label="vid-seqseries-ratroot-root-test"/>
     </figure>
diff --git a/ptx/sec_riemann.ptx b/ptx/sec_riemann.ptx
index c65ccce77..a4fa817de 100644
--- a/ptx/sec_riemann.ptx
+++ b/ptx/sec_riemann.ptx
@@ -1535,7 +1535,7 @@
           </md>.
         </p>
       </solution>
-      <solution component="video" vshift="7">
+      <solution component="video" vshift="8">
         <title>Video solution</title>
         <video width="98%" youtube="yvWSszI0Xvc" label="vid_int_rie_ex_lim" component="video"/>
       </solution>
diff --git a/ptx/sec_sequences.ptx b/ptx/sec_sequences.ptx
index 7198944ad..88c37342d 100644
--- a/ptx/sec_sequences.ptx
+++ b/ptx/sec_sequences.ptx
@@ -309,7 +309,7 @@
         </ol>
       </p>
     </solution>
-    <solution component="video" vshift="9">
+    <solution component="video" vshift="18">
       <title>Video solution</title>
       <video width="98%" youtube="j-iqXR_bANY" label="vid-seqseries-sequences-example1" component="video"/>
     </solution>
@@ -1450,7 +1450,7 @@
     </p>
   </aside>
 
-  <figure xml:id="vid-seqseries-sequences-monotone-bounded" component="video" vshift="1">
+  <figure xml:id="vid-seqseries-sequences-monotone-bounded" component="video" vshift="-2">
     <caption>Video presentation of <xref ref="def_monotonic"/> and <xref ref="thm_monotonic_converge"/></caption>
     <video youtube="ZxaUovyGMBI" label="vid-seqseries-sequences-monotone-bounded"/>
   </figure>
diff --git a/ptx/sec_series.ptx b/ptx/sec_series.ptx
index bba19d7cc..b4b4a0316 100644
--- a/ptx/sec_series.ptx
+++ b/ptx/sec_series.ptx
@@ -718,7 +718,7 @@
           </ol>
         </p>
       </solution>
-      <solution component="video" vshift="13">
+      <solution component="video" vshift="20">
         <title>Video solution</title>
         <video width="98%" youtube="9_AmxyiKVm8" label="vid-seqseries-sequences-example-geometric" component="video"/>
       </solution>
diff --git a/ptx/sec_space_coord.ptx b/ptx/sec_space_coord.ptx
index 93eb2cd27..f77920f3c 100644
--- a/ptx/sec_space_coord.ptx
+++ b/ptx/sec_space_coord.ptx
@@ -746,7 +746,7 @@
           <!-- figures/figspace3_3D.asy END -->
         </figure>
       </solution>
-      <solution component="video" vshift="2">
+      <solution component="video" vshift="6">
         <title>Video solution</title>
         <video width="98%" youtube="-9luj-GlMqA" label="vid-vectors-spacecoord-planes-eg" component="video"/>
       </solution>
diff --git a/ptx/sec_stokes_divergence.ptx b/ptx/sec_stokes_divergence.ptx
index 873a934a5..802410e0e 100644
--- a/ptx/sec_stokes_divergence.ptx
+++ b/ptx/sec_stokes_divergence.ptx
@@ -685,6 +685,9 @@
       one has power to select the easiest computation as illustrated next.
     </p>
 
+
+        <enlarge-page skipsize="4"/>
+
     <example xml:id="ex_divthm_space4">
       <title>Using the Divergence Theorem to compute flux</title>
       <statement>
@@ -705,8 +708,6 @@
           </md>.
         </p>
 
-        <enlarge-page skipsize="2"/>
-
         <p>
           The direct flux computation requires six surface integrals,
           one for each face of the cube.
diff --git a/ptx/sec_tan_norm.ptx b/ptx/sec_tan_norm.ptx
index 6f2293ae0..098580294 100644
--- a/ptx/sec_tan_norm.ptx
+++ b/ptx/sec_tan_norm.ptx
@@ -140,7 +140,7 @@
           <m>\unittangent(1)</m> to verify it has length 1.
         </p>
       </solution>
-      <solution component="video" vshift="8">
+      <solution component="video" vshift="9">
         <title>Video solution</title>
         <video width="98%" youtube="aGEMbQrBpPI" label="vid-vvf-tannorm-tangent-eg1" component="video"/>
       </solution>
@@ -229,7 +229,7 @@
           <!-- figures/fig_tannorm2.tex END -->
         </figure>
       </solution>
-      <solution component="video" vshift="5.5">
+      <solution component="video" vshift="7">
         <title>Video solution</title>
         <video width="98%" youtube="zdfMTWdXzJs" label="vid-vvf-tannorm-tangent-eg2" component="video"/>
       </solution>
@@ -441,7 +441,7 @@
           <!-- figures/figtannorm3_3D.asy END -->
         </figure>
       </solution>
-      <solution component="video" vshift="4">
+      <solution component="video" vshift="6">
         <title>Video solution</title>
         <video width="98%" youtube="cZkvyF0t5P4" label="vid-vvf-tannorm-normal-eg1" component="video"/>
       </solution>
@@ -846,7 +846,7 @@
           Here the particle's speed is not changing and all acceleration is in the form of direction change.
         </p>
       </solution>
-      <solution component="video" vshift="5">
+      <solution component="video" vshift="6">
         <title>Video solution</title>
         <video width="98%" youtube="8LTqjQPvh-A" label="vid-vvf-tannorm-accel-eg2" component="video"/>
       </solution>
diff --git a/ptx/sec_taylor_poly.ptx b/ptx/sec_taylor_poly.ptx
index 2be67c0e3..035a6e9aa 100644
--- a/ptx/sec_taylor_poly.ptx
+++ b/ptx/sec_taylor_poly.ptx
@@ -223,7 +223,67 @@
       whose first four derivatives at 0 match those of <m>f</m>.
     </p>
 
-    <figure xml:id="fig_taypolyintrob" vshift="1">
+    <figure xml:id="fig_taypolyintrob" vshift="1" component="taypoly-late">
+      <caption>Plotting <m>f</m>, <m>p_2</m> and <m>p_4</m></caption>
+      <!-- START figures/fig_taypolyintrob.tex -->
+      <image width="47%">
+        <shortdescription>The graph of a function and two polynomials that approximate the function near x=0.</shortdescription>
+        <description>
+          <p>
+            The graph of a function <m>f(x)</m> is shown. It is the same function as the first image in this section,
+            but again, the precise details of the graph are unimportant.
+          </p>
+
+          <p>
+            Also shown are the graphs of two functions <m>p_2(x)</m> and <m>p_4(x)</m>.
+            The function <m>p_2(x)</m> is quadratic, and its graph is a parabola that opens upward.
+            The function <m>p_4(x)</m> is a polynomial of degree 4.
+          </p>
+
+          <p>
+            All three graphs intersect at the point <m>(0,f(0))</m>,
+            and the values of both <m>p_2(x)</m> and <m>p_4(x)</m> are close to the value of <m>f(x)</m> when <m>x</m> is close to <m>0</m>.
+            Two observations are important: first, both of these polynomial graphs appear to lie more closely to the graph of <m>f(x)</m>
+            than the tangent line in the first image. Second, the graph of <m>p_4(x)</m> is a good approximation to <m>f(x)</m>
+            over a larger interval than the graph of <m>p_2(x)</m>.
+          </p>
+
+          <p>
+            In particular, the point <m>(0,f(0))</m> appears to be a local minimum,
+            and there is a corresponding minimum in the graphs of both <m>p_2(x)</m> and <m>p_4(x)</m>.
+            But the graph of <m>f(x)</m> also appears to have a local maximum near <m>x=1</m>.
+            Near <m>x=1</m>, the graph of <m>p_2(x)</m> separates from that of <m>f(x)</m>:
+            the first continues to increase, while the second begins to decrease.
+            Near <m>x=1</m>, <m>p_2(x)</m> is no longer a good approximation to <m>f(x)</m>.
+          </p>
+
+          <p>
+            However, the graph of <m>p_4(x)</m> also has a maximum near <m>x=1</m>,
+            and <m>p_4(x)</m> appears to be a good approximation to <m>f(x)</m> at least until <m>x=2</m>.
+          </p>
+        </description>
+        <latex-image label="img_taypolyintrob">
+          \begin{tikzpicture}
+
+          \begin{axis}[
+          axis on top,
+          ymin=-5.5,ymax=8.5,
+          xmin=-4.5,xmax=4.4
+          ]
+
+          \addplot+ [infinite,domain=-4:3.2,samples=120] {exp(x)*sin(deg(x))*cos(deg(x))+2} node [pos=0.6,left] { $y=f(x)$};
+          \addplot+ [domain=-3:2] {x^2+x+2} node [pos=0.2, below left] { $y=p_2(x)$};
+          \addplot+ [domain=-2:2] {-x^4/2-x^3/6+x^2+x+2} node [pos=0.1, below left] { $y=p_4(x)$};
+
+          \end{axis}
+
+          \end{tikzpicture}
+        </latex-image>
+      </image>
+      <!-- figures/fig_taypolyintrob.tex END -->
+    </figure>
+
+    <figure xml:id="fig_taypolyintrob" vshift="-1" component="taypoly-early">
       <caption>Plotting <m>f</m>, <m>p_2</m> and <m>p_4</m></caption>
       <!-- START figures/fig_taypolyintrob.tex -->
       <image width="47%">
@@ -1612,7 +1672,7 @@
                 </tabular> -->
               </figure>
 
-              <figure xml:id="fig_taypoly5a-early" vshift="-4.5" component="taypoly-early">
+              <figure xml:id="fig_taypoly5a-early" vshift="-3.5" component="taypoly-early">
                 <caption>A table of the derivatives of <m>f(x)=\sqrt{x}</m> evaluated at <m>x=4</m></caption>
                 <sidebyside>
                   <p>
diff --git a/ptx/sec_transformations.ptx b/ptx/sec_transformations.ptx
index 8123fee20..4796a64d4 100644
--- a/ptx/sec_transformations.ptx
+++ b/ptx/sec_transformations.ptx
@@ -2142,7 +2142,7 @@
 					Thus the desired transformation is defined on the rectangle <m>D = [1,4]\times [1,2]</m> and has an inverse given by <m>T^{-1}(x,y) = (y/x,xy)</m>.
 				</p>
 
-				<figure xml:id="fig_int_trans2" vshift="0">
+				<figure xml:id="fig_int_trans2" vshift="2">
 					<caption>The region of integration in <xref ref="ex_int_trans2"/></caption>
 					<image width="47%">
 						<shortdescription>A region in the first quadrant bounded by two hyperbolas, and two lines through the origin.</shortdescription>
diff --git a/ptx/sec_trigint.ptx b/ptx/sec_trigint.ptx
index 0c84af962..74d1c8129 100644
--- a/ptx/sec_trigint.ptx
+++ b/ptx/sec_trigint.ptx
@@ -832,7 +832,7 @@
           </md>.
         </p>
       </solution>
-      <solution component="video" vshift="-2">
+      <solution component="video" vshift="2">
         <title>Video solution</title>
         <video width="98%" youtube="MUDKKDz3_C8" label="vid-int-trig-ex-tan6" component="video"/>
       </solution>
diff --git a/ptx/sec_vector_intro.ptx b/ptx/sec_vector_intro.ptx
index 6d8469ef0..5a3dfcd16 100644
--- a/ptx/sec_vector_intro.ptx
+++ b/ptx/sec_vector_intro.ptx
@@ -511,7 +511,7 @@
     <q>component-wise.</q>
   </p>
 
-  <figure xml:id="vid-vectors-intro-algebra" component="video" vshift="5">
+  <figure xml:id="vid-vectors-intro-algebra" component="video" vshift="8">
     <caption>Video presentation of <xref ref="def_vector_algebra"/> (2 videos)</caption>
     <video youtube="tOpeq-_K0ME" label="vid-vectors-intro-algebra"/>
   </figure>
@@ -578,7 +578,7 @@
         These are all sketched in <xref ref="fig_vect2"/>.
       </p>
     </solution>
-    <solution component="video" vshift="4">
+    <solution component="video" vshift="8">
       <title>Video solution</title>
       <video width="98%" youtube="3MSwQJq_3s0" label="vid-vectors-intro-addition" component="video"/>
     </solution>
@@ -771,7 +771,7 @@
         (when their initial points are the same).
       </p>
     </solution>
-    <solution component="video" vshift="0">
+    <solution component="video" vshift="-1">
       <title>Video solution</title>
       <video width="98%" youtube="a_qRwTkQXYQ" label="vid-vectors-intro-subtraction" component="video"/>
     </solution>
@@ -1128,7 +1128,7 @@
         </ol>
       </p>
     </solution>
-    <solution component="video" vshift="5">
+    <solution component="video" vshift="9">
       <title>Video solution</title>
       <video width="98%" youtube="B9OV0Dja6IY" label="vid-vectors-intro-unitvec-eg" component="video"/>
     </solution>
diff --git a/ptx/sec_vvf.ptx b/ptx/sec_vvf.ptx
index 46ccae9c2..5b7671aaa 100644
--- a/ptx/sec_vvf.ptx
+++ b/ptx/sec_vvf.ptx
@@ -632,7 +632,7 @@
           <m>\vec r(t) = \vec p(t) + \vec c(t) = \la \cos(t) + t,-\sin(t) +1\ra</m>,
           which is graphed in <xref ref="fig_vvf4b"/>.
         </p>
-        <figure xml:id="fig_vvf4b" vshift="-3">
+        <figure xml:id="fig_vvf4b" vshift="2">
           <caption>The cycloid in <xref ref="ex_vvf4"/></caption>
           <!-- START figures/fig_vvf4a.tex -->
           <image width="47%">
@@ -663,7 +663,7 @@
           <!-- figures/fig_vvf4a.tex END -->
         </figure>
       </solution>
-      <solution component="video" vshift="3">
+      <solution component="video" vshift="7.5">
         <title>Video solution</title>
         <video width="98%" youtube="BH9FZMTdgQw" label="vid-vvf-vvfintro-cycloid" component="video"/>
       </solution>
@@ -702,7 +702,7 @@
       </statement>
     </definition>
 
-    <figure xml:id="vid-vvf-vvfintro-displacement" component="video" vshift="-3">
+    <figure xml:id="vid-vvf-vvfintro-displacement" component="video" vshift="2">
       <caption>Video presentation of <xref ref="def_displacement"/></caption>
       <video youtube="LfOpC91t7H8" label="vid-vvf-vvfintro-displacement"/>
     </figure>
@@ -851,7 +851,7 @@
           this average rate of change on <m>[-1,5]</m> is <m>1/3</m> the average rate of change on <m>[-1,1]</m>.
         </p>
       </solution>
-      <solution component="video" vshift="3">
+      <solution component="video" vshift="0">
         <title>Video solution</title>
         <video width="98%" youtube="REA-v1g68bo" label="vid-vvf-vvfintro-average" component="video"/>
       </solution>
diff --git a/ptx/sec_vvf_calc.ptx b/ptx/sec_vvf_calc.ptx
index f5aea28b6..66bf615b8 100644
--- a/ptx/sec_vvf_calc.ptx
+++ b/ptx/sec_vvf_calc.ptx
@@ -835,7 +835,7 @@
           hence cannot find the equation of the tangent line.
         </p>
       </solution>
-      <solution component="video" vshift="3">
+      <solution component="video" vshift="2.5">
         <title>Video solution</title>
         <video width="98%" youtube="czvJ5AtLpa4" label="vid-vvf-calc-tangent-eg2" component="video"/>
       </solution>
diff --git a/ptx/sec_vvf_motion.ptx b/ptx/sec_vvf_motion.ptx
index 4f219e34a..4e8e03724 100644
--- a/ptx/sec_vvf_motion.ptx
+++ b/ptx/sec_vvf_motion.ptx
@@ -1210,7 +1210,7 @@
           </ol>
         </p>
       </solution>
-      <solution component="video" vshift="7">
+      <solution component="video" vshift="9">
         <title>Video solution</title>
         <video width="98%" youtube="vLSocZ7XLQM" label="vid-vvf-motion-distance-eg" component="video"/>
       </solution>
diff --git a/publication/publication-accelerated-print.ptx b/publication/publication-accelerated-print.ptx
index 13e918e32..8651cb756 100644
--- a/publication/publication-accelerated-print.ptx
+++ b/publication/publication-accelerated-print.ptx
@@ -31,6 +31,17 @@
       <page>
         <geometry>inner=1in,textheight=9in,textwidth=320pt,marginparwidth=150pt,marginparsep=20pt,bottom=1in,footskip=29pt</geometry>
       </page>
+      <!-- page breaks in sections -->
+      <insertions pagebreaks="p-antider-break1 thm_deriv_glossary fig_disk0a fig_dotp3 fig_iterated6 fig_lines2 paragraphs-newton-convergence"/>
+      <insertions pagebreaks="fig_polar_roses subsec-series idea_shell_and_washer def_triple_integral_2 def_parallel_vectors fig_motion2a subsec-common-thread"/>
+      <insertions pagebreaks="riemann-summary-break subsec-polar-graphs thm_continuity_algebra def_infl thm_second_der thm_multi_second_test ex_iterated6"/>
+      <insertions pagebreaks="reference-area-volume reference-algebra reference-formulas reference-series-tests sec-hessian sec-multi_extreme_further"/>
+       <!-- page breaks in exercises. -->
+      <insertions pagebreaks="exset-deriv-implicit-tangent exset-definite-integral-area exset-definite-integral-velocity exset-definite-integral-properties"/>
+      <insertions pagebreaks="exset-riemann-integral-approx x07_01_ex_29 exset-alternating-series-bound-sum exset-conic-hyperbola-eqn-std"/>
+      <insertions pagebreaks="exset-parametric-describe-rectangular exset-vector-sum-sketch exset-limit-continuity-point exset-deriv-basic-higher"/>
+      <insertions pagebreaks="exset-trig-sub-definite exset-volume-shells-x-axis exset-power-series-find-series exset-cross-product-quadrilateral"/>
+      <insertions pagebreaks="exset-double-polar-special exset-cylindrical-spherical-setup exset-Greens-divergence exset-vectors-balance-forces"/>
     </latex>
     <epub>
       <cover front="cover/cover.png"/>
diff --git a/publication/publication-accelerated.ptx b/publication/publication-accelerated.ptx
index 6d6abd6c1..7af37aa7a 100644
--- a/publication/publication-accelerated.ptx
+++ b/publication/publication-accelerated.ptx
@@ -33,6 +33,17 @@
       <page>
         <geometry>inner=1in,textheight=9in,textwidth=320pt,marginparwidth=150pt,marginparsep=20pt,bottom=1in,footskip=29pt</geometry>
       </page>
+      <!-- page breaks in sections -->
+      <insertions pagebreaks="p-antider-break1 thm_deriv_glossary fig_disk0a fig_dotp3 fig_iterated6 fig_lines2 paragraphs-newton-convergence"/>
+      <insertions pagebreaks="fig_polar_roses subsec-series idea_shell_and_washer def_triple_integral_2 def_parallel_vectors fig_motion2a subsec-common-thread"/>
+      <insertions pagebreaks="riemann-summary-break subsec-polar-graphs thm_continuity_algebra def_infl thm_second_der thm_multi_second_test ex_iterated6"/>
+      <insertions pagebreaks="reference-area-volume reference-algebra reference-formulas reference-series-tests sec-hessian sec-multi_extreme_further"/>
+       <!-- page breaks in exercises. -->
+      <insertions pagebreaks="exset-deriv-implicit-tangent exset-definite-integral-area exset-definite-integral-velocity exset-definite-integral-properties"/>
+      <insertions pagebreaks="exset-riemann-integral-approx x07_01_ex_29 exset-alternating-series-bound-sum exset-conic-hyperbola-eqn-std"/>
+      <insertions pagebreaks="exset-parametric-describe-rectangular exset-vector-sum-sketch exset-limit-continuity-point exset-deriv-basic-higher"/>
+      <insertions pagebreaks="exset-trig-sub-definite exset-volume-shells-x-axis exset-power-series-find-series exset-cross-product-quadrilateral"/>
+      <insertions pagebreaks="exset-double-polar-special exset-cylindrical-spherical-setup exset-Greens-divergence exset-vectors-balance-forces"/>
     </latex>
     <epub>
       <cover front="cover/cover.png"/>
diff --git a/publication/publication-color-print-novideo.ptx b/publication/publication-color-print-novideo.ptx
index 85bc223d6..f912b3788 100644
--- a/publication/publication-color-print-novideo.ptx
+++ b/publication/publication-color-print-novideo.ptx
@@ -36,12 +36,13 @@
       <insertions pagebreaks="p-antider-break1 thm_deriv_glossary fig_disk0a fig_dotp3 fig_iterated6 fig_lines2 paragraphs-newton-convergence"/>
       <insertions pagebreaks="fig_polar_roses subsec-series idea_shell_and_washer def_triple_integral_2 def_parallel_vectors fig_motion2a subsec-common-thread"/>
       <insertions pagebreaks="riemann-summary-break subsec-polar-graphs thm_continuity_algebra def_infl thm_second_der thm_multi_second_test ex_iterated6"/>
+      <insertions pagebreaks="reference-area-volume reference-algebra reference-formulas reference-series-tests"/>
        <!-- page breaks in exercises. -->
       <insertions pagebreaks="exset-deriv-implicit-tangent exset-definite-integral-area exset-definite-integral-velocity exset-definite-integral-properties"/>
       <insertions pagebreaks="exset-riemann-integral-approx x07_01_ex_29 exset-alternating-series-bound-sum exset-conic-hyperbola-eqn-std"/>
       <insertions pagebreaks="exset-parametric-describe-rectangular exset-vector-sum-sketch exset-limit-continuity-point exset-deriv-basic-higher"/>
       <insertions pagebreaks="exset-trig-sub-definite exset-volume-shells-x-axis exset-power-series-find-series exset-cross-product-quadrilateral"/>
-      <insertions pagebreaks="exset-double-polar-special exset-cylindrical-spherical-setup exset-Greens-divergence"/>
+      <insertions pagebreaks="exset-double-polar-special exset-cylindrical-spherical-setup exset-Greens-divergence exset-vectors-balance-forces"/>
     </latex>
     <epub>
       <cover front="cover/cover.png"/>
diff --git a/publication/publication-color-print.ptx b/publication/publication-color-print.ptx
index 48d49d07a..507eca85a 100644
--- a/publication/publication-color-print.ptx
+++ b/publication/publication-color-print.ptx
@@ -32,6 +32,16 @@
       <page>
         <geometry>inner=1in,textheight=9in,textwidth=320pt,marginparwidth=150pt,marginparsep=20pt,bottom=1in,footskip=29pt</geometry>
       </page>
+      <insertions pagebreaks="p-antider-break1 thm_deriv_glossary fig_disk0a fig_dotp3 fig_iterated6 fig_lines2 paragraphs-newton-convergence"/>
+      <insertions pagebreaks="fig_polar_roses subsec-series idea_shell_and_washer def_triple_integral_2 def_parallel_vectors fig_motion2a subsec-common-thread"/>
+      <insertions pagebreaks="riemann-summary-break subsec-polar-graphs thm_continuity_algebra def_infl thm_second_der thm_multi_second_test ex_iterated6"/>
+      <insertions pagebreaks="reference-area-volume reference-algebra reference-formulas reference-series-tests"/>
+       <!-- page breaks in exercises. -->
+      <insertions pagebreaks="exset-deriv-implicit-tangent exset-definite-integral-area exset-definite-integral-velocity exset-definite-integral-properties"/>
+      <insertions pagebreaks="exset-riemann-integral-approx x07_01_ex_29 exset-alternating-series-bound-sum exset-conic-hyperbola-eqn-std"/>
+      <insertions pagebreaks="exset-parametric-describe-rectangular exset-vector-sum-sketch exset-limit-continuity-point exset-deriv-basic-higher"/>
+      <insertions pagebreaks="exset-trig-sub-definite exset-volume-shells-x-axis exset-power-series-find-series exset-cross-product-quadrilateral"/>
+      <insertions pagebreaks="exset-double-polar-special exset-cylindrical-spherical-setup exset-Greens-divergence exset-vectors-balance-forces"/>
     </latex>
     <epub>
       <cover front="cover/cover.png"/>
diff --git a/publication/publication-novid-print.ptx b/publication/publication-novid-print.ptx
index 33f3a70ab..7fd1f28df 100644
--- a/publication/publication-novid-print.ptx
+++ b/publication/publication-novid-print.ptx
@@ -34,12 +34,13 @@
       <insertions pagebreaks="p-antider-break1 thm_deriv_glossary fig_disk0a fig_dotp3 fig_iterated6 fig_lines2 paragraphs-newton-convergence"/>
       <insertions pagebreaks="fig_polar_roses subsec-series idea_shell_and_washer def_triple_integral_2 def_parallel_vectors fig_motion2a subsec-common-thread"/>
       <insertions pagebreaks="riemann-summary-break subsec-polar-graphs thm_continuity_algebra def_infl thm_second_der thm_multi_second_test ex_iterated6"/>
+      <insertions pagebreaks="reference-area-volume reference-algebra reference-formulas reference-series-tests"/>
        <!-- page breaks in exercises. -->
       <insertions pagebreaks="exset-deriv-implicit-tangent exset-definite-integral-area exset-definite-integral-velocity exset-definite-integral-properties"/>
       <insertions pagebreaks="exset-riemann-integral-approx x07_01_ex_29 exset-alternating-series-bound-sum exset-conic-hyperbola-eqn-std"/>
       <insertions pagebreaks="exset-parametric-describe-rectangular exset-vector-sum-sketch exset-limit-continuity-point exset-deriv-basic-higher"/>
       <insertions pagebreaks="exset-trig-sub-definite exset-volume-shells-x-axis exset-power-series-find-series exset-cross-product-quadrilateral"/>
-      <insertions pagebreaks="exset-double-polar-special exset-cylindrical-spherical-setup exset-Greens-divergence"/>
+      <insertions pagebreaks="exset-double-polar-special exset-cylindrical-spherical-setup exset-Greens-divergence exset-vectors-balance-forces"/>
     </latex>
     <epub>
       <cover front="cover/cover.png"/>
diff --git a/publication/publication-novid.ptx b/publication/publication-novid.ptx
index 81f9cacda..6638e9f0a 100644
--- a/publication/publication-novid.ptx
+++ b/publication/publication-novid.ptx
@@ -32,6 +32,16 @@
       <page>
         <geometry>inner=1in,textheight=9in,textwidth=320pt,marginparwidth=150pt,marginparsep=20pt,bottom=1in,footskip=29pt</geometry>
       </page>
+      <insertions pagebreaks="p-antider-break1 thm_deriv_glossary fig_disk0a fig_dotp3 fig_iterated6 fig_lines2 paragraphs-newton-convergence"/>
+      <insertions pagebreaks="fig_polar_roses subsec-series idea_shell_and_washer def_triple_integral_2 def_parallel_vectors fig_motion2a subsec-common-thread"/>
+      <insertions pagebreaks="riemann-summary-break subsec-polar-graphs thm_continuity_algebra def_infl thm_second_der thm_multi_second_test ex_iterated6"/>
+      <insertions pagebreaks="reference-area-volume reference-algebra reference-formulas reference-series-tests"/>
+       <!-- page breaks in exercises. -->
+      <insertions pagebreaks="exset-deriv-implicit-tangent exset-definite-integral-area exset-definite-integral-velocity exset-definite-integral-properties"/>
+      <insertions pagebreaks="exset-riemann-integral-approx x07_01_ex_29 exset-alternating-series-bound-sum exset-conic-hyperbola-eqn-std"/>
+      <insertions pagebreaks="exset-parametric-describe-rectangular exset-vector-sum-sketch exset-limit-continuity-point exset-deriv-basic-higher"/>
+      <insertions pagebreaks="exset-trig-sub-definite exset-volume-shells-x-axis exset-power-series-find-series exset-cross-product-quadrilateral"/>
+      <insertions pagebreaks="exset-double-polar-special exset-cylindrical-spherical-setup exset-Greens-divergence exset-vectors-balance-forces"/>
     </latex>
     <epub>
       <cover front="cover/cover.png"/>
diff --git a/publication/publication-standard-print.ptx b/publication/publication-standard-print.ptx
index 28df14e07..c0d4f1e12 100644
--- a/publication/publication-standard-print.ptx
+++ b/publication/publication-standard-print.ptx
@@ -31,6 +31,17 @@
       <page>
         <geometry>inner=1in,textheight=9in,textwidth=320pt,marginparwidth=150pt,marginparsep=20pt,bottom=1in,footskip=29pt</geometry>
       </page>
+      <!-- page breaks in sections -->
+      <insertions pagebreaks="p-antider-break1 thm_deriv_glossary fig_disk0a fig_dotp3 fig_iterated6 fig_lines2 paragraphs-newton-convergence"/>
+      <insertions pagebreaks="fig_polar_roses subsec-series idea_shell_and_washer def_triple_integral_2 def_parallel_vectors fig_motion2a subsec-common-thread"/>
+      <insertions pagebreaks="riemann-summary-break subsec-polar-graphs thm_continuity_algebra def_infl thm_second_der thm_multi_second_test ex_iterated6"/>
+      <insertions pagebreaks="reference-area-volume reference-algebra reference-formulas reference-series-tests sec-hessian sec-multi_extreme_further"/>
+       <!-- page breaks in exercises. -->
+      <insertions pagebreaks="exset-deriv-implicit-tangent exset-definite-integral-area exset-definite-integral-velocity exset-definite-integral-properties"/>
+      <insertions pagebreaks="exset-riemann-integral-approx x07_01_ex_29 exset-alternating-series-bound-sum exset-conic-hyperbola-eqn-std"/>
+      <insertions pagebreaks="exset-parametric-describe-rectangular exset-vector-sum-sketch exset-limit-continuity-point exset-deriv-basic-higher"/>
+      <insertions pagebreaks="exset-trig-sub-definite exset-volume-shells-x-axis exset-power-series-find-series exset-cross-product-quadrilateral"/>
+      <insertions pagebreaks="exset-double-polar-special exset-cylindrical-spherical-setup exset-Greens-divergence exset-vectors-balance-forces"/>
     </latex>
     <epub>
       <cover front="cover/cover.png"/>
diff --git a/publication/publication-standard.ptx b/publication/publication-standard.ptx
index ea2b6a5bb..af63f3d02 100644
--- a/publication/publication-standard.ptx
+++ b/publication/publication-standard.ptx
@@ -33,6 +33,17 @@
       <page>
         <geometry>inner=1in,textheight=9in,textwidth=320pt,marginparwidth=150pt,marginparsep=20pt,bottom=1in,footskip=29pt</geometry>
       </page>
+      <!-- page breaks in sections -->
+      <insertions pagebreaks="p-antider-break1 thm_deriv_glossary fig_disk0a fig_dotp3 fig_iterated6 fig_lines2 paragraphs-newton-convergence"/>
+      <insertions pagebreaks="fig_polar_roses subsec-series idea_shell_and_washer def_triple_integral_2 def_parallel_vectors fig_motion2a subsec-common-thread"/>
+      <insertions pagebreaks="riemann-summary-break subsec-polar-graphs thm_continuity_algebra def_infl thm_second_der thm_multi_second_test ex_iterated6"/>
+      <insertions pagebreaks="reference-area-volume reference-algebra reference-formulas reference-series-tests sec-hessian sec-multi_extreme_further"/>
+       <!-- page breaks in exercises. -->
+      <insertions pagebreaks="exset-deriv-implicit-tangent exset-definite-integral-area exset-definite-integral-velocity exset-definite-integral-properties"/>
+      <insertions pagebreaks="exset-riemann-integral-approx x07_01_ex_29 exset-alternating-series-bound-sum exset-conic-hyperbola-eqn-std"/>
+      <insertions pagebreaks="exset-parametric-describe-rectangular exset-vector-sum-sketch exset-limit-continuity-point exset-deriv-basic-higher"/>
+      <insertions pagebreaks="exset-trig-sub-definite exset-volume-shells-x-axis exset-power-series-find-series exset-cross-product-quadrilateral"/>
+      <insertions pagebreaks="exset-double-polar-special exset-cylindrical-spherical-setup exset-Greens-divergence exset-vectors-balance-forces"/>
     </latex>
     <epub>
       <cover front="cover/cover.png"/>
diff --git a/publication/publication.ptx b/publication/publication.ptx
index f6ab24cf8..48ada9344 100644
--- a/publication/publication.ptx
+++ b/publication/publication.ptx
@@ -33,6 +33,17 @@
       <page>
         <geometry>inner=1in,textheight=9in,textwidth=320pt,marginparwidth=150pt,marginparsep=20pt,bottom=1in,footskip=29pt</geometry>
       </page>
+      <!-- page breaks in sections -->
+      <insertions pagebreaks="p-antider-break1 thm_deriv_glossary fig_disk0a fig_dotp3 fig_iterated6 fig_lines2 paragraphs-newton-convergence"/>
+      <insertions pagebreaks="fig_polar_roses subsec-series idea_shell_and_washer def_triple_integral_2 def_parallel_vectors fig_motion2a subsec-common-thread"/>
+      <insertions pagebreaks="riemann-summary-break subsec-polar-graphs thm_continuity_algebra def_infl thm_second_der thm_multi_second_test ex_iterated6"/>
+      <insertions pagebreaks="reference-area-volume reference-algebra reference-formulas reference-series-tests"/>
+       <!-- page breaks in exercises. -->
+      <insertions pagebreaks="exset-deriv-implicit-tangent exset-definite-integral-area exset-definite-integral-velocity exset-definite-integral-properties"/>
+      <insertions pagebreaks="exset-riemann-integral-approx x07_01_ex_29 exset-alternating-series-bound-sum exset-conic-hyperbola-eqn-std"/>
+      <insertions pagebreaks="exset-parametric-describe-rectangular exset-vector-sum-sketch exset-limit-continuity-point exset-deriv-basic-higher"/>
+      <insertions pagebreaks="exset-trig-sub-definite exset-volume-shells-x-axis exset-power-series-find-series exset-cross-product-quadrilateral"/>
+      <insertions pagebreaks="exset-double-polar-special exset-cylindrical-spherical-setup exset-Greens-divergence exset-vectors-balance-forces"/>
     </latex>
     <epub>
       <cover front="cover/cover.png"/>
diff --git a/xsl/apex-latex-print-color.xsl b/xsl/apex-latex-print-color.xsl
index 4110e787f..eacab6ce6 100644
--- a/xsl/apex-latex-print-color.xsl
+++ b/xsl/apex-latex-print-color.xsl
@@ -423,7 +423,7 @@ https://tex.stackexchange.com/questions/605955/can-i-avoid-indentation-of-margin
 <xsl:template match="aside">
     <xsl:text>&#xa;</xsl:text>
     <xsl:choose>
-      <xsl:when test="ancestor::example and not(ancestor::ul or ancestor::ol)">
+      <xsl:when test="(ancestor::example or ancestor::insight) and not(ancestor::ul or ancestor::ol)">
         <xsl:text>\tcbmarginbox{%&#xa;</xsl:text>
       </xsl:when>
       <xsl:when test="(ancestor::example or ancestor::theorem) and (ancestor::ul or ancestor::ol)">
@@ -470,7 +470,7 @@ https://tex.stackexchange.com/questions/605955/can-i-avoid-indentation-of-margin
 
   <!-- give video a new name so it escapes assembly -->
   <margin-video>
-    <image width="40%" margins="2% 58%">
+    <image width="30%" margins="6% 64%">
       <xsl:attribute name="pi:generated">
           <xsl:text>qrcode/</xsl:text>
           <xsl:apply-templates select="." mode="assembly-id"/>
diff --git a/xsl/apex-latex-print-style.xsl b/xsl/apex-latex-print-style.xsl
index 4629b4060..4566a26a7 100644
--- a/xsl/apex-latex-print-style.xsl
+++ b/xsl/apex-latex-print-style.xsl
@@ -423,7 +423,7 @@ https://tex.stackexchange.com/questions/605955/can-i-avoid-indentation-of-margin
 <xsl:template match="aside">
     <xsl:text>&#xa;</xsl:text>
     <xsl:choose>
-      <xsl:when test="ancestor::example and not(ancestor::ul or ancestor::ol)">
+      <xsl:when test="(ancestor::example or ancestor::insight) and not(ancestor::ul or ancestor::ol)">
         <xsl:text>\tcbmarginbox{%&#xa;</xsl:text>
       </xsl:when>
       <xsl:when test="(ancestor::example or ancestor::theorem) and (ancestor::ul or ancestor::ol)">
@@ -470,7 +470,7 @@ https://tex.stackexchange.com/questions/605955/can-i-avoid-indentation-of-margin
 
   <!-- give video a new name so it escapes assembly -->
   <margin-video>
-    <image width="40%" margins="2% 58%">
+    <image width="30%" margins="6% 64%">
       <xsl:attribute name="pi:generated">
           <xsl:text>qrcode/</xsl:text>
           <xsl:apply-templates select="." mode="assembly-id"/>
diff --git a/xsl/apex-latex-style.xsl b/xsl/apex-latex-style.xsl
index d1b29ef22..418d99591 100644
--- a/xsl/apex-latex-style.xsl
+++ b/xsl/apex-latex-style.xsl
@@ -406,7 +406,7 @@ https://tex.stackexchange.com/questions/605955/can-i-avoid-indentation-of-margin
 <xsl:template match="aside">
     <xsl:text>&#xa;</xsl:text>
     <xsl:choose>
-      <xsl:when test="ancestor::example and not(ancestor::ul or ancestor::ol)">
+      <xsl:when test="(ancestor::example or ancestor::insight) and not(ancestor::ul or ancestor::ol)">
         <xsl:text>\tcbmarginbox{%&#xa;</xsl:text>
       </xsl:when>
       <xsl:when test="(ancestor::example or ancestor::theorem) and (ancestor::ul or ancestor::ol)">
@@ -453,7 +453,7 @@ https://tex.stackexchange.com/questions/605955/can-i-avoid-indentation-of-margin
 
   <!-- give video a new name so it escapes assembly -->
   <margin-video>
-    <image width="40%" margins="2% 58%">
+    <image width="30%" margins="6% 64%">
       <xsl:attribute name="pi:generated">
           <xsl:text>qrcode/</xsl:text>
           <xsl:apply-templates select="." mode="assembly-id"/>

From 67add17ddd3280bcffa1f06c59e18a56b5cd316b Mon Sep 17 00:00:00 2001
From: sean-fitzpatrick <sean.fitzpatrick@uleth.ca>
Date: Fri, 5 Jun 2026 16:13:03 -0600
Subject: [PATCH 18/18] a few more adjustments

---
 ptx/sec_cylindrical_spherical.ptx | 38 +++++++++++++++++++++++++++++--
 ptx/sec_double_int_volume.ptx     |  2 +-
 ptx/sec_line_int_vf.ptx           | 10 ++++----
 ptx/sec_multi_chain.ptx           | 10 ++++----
 ptx/sec_planes.ptx                |  8 +++----
 ptx/sec_ratio_root_tests.ptx      | 10 ++++----
 ptx/sec_space_coord.ptx           |  4 ++--
 ptx/sec_taylor_poly.ptx           |  2 +-
 ptx/sec_taylor_series.ptx         |  2 +-
 ptx/sec_trigint.ptx               | 24 ++++++++++---------
 ptx/sec_triple_int.ptx            | 26 ++++++++++++++++++++-
 11 files changed, 98 insertions(+), 38 deletions(-)

diff --git a/ptx/sec_cylindrical_spherical.ptx b/ptx/sec_cylindrical_spherical.ptx
index 1ed8da025..ec45b395d 100644
--- a/ptx/sec_cylindrical_spherical.ptx
+++ b/ptx/sec_cylindrical_spherical.ptx
@@ -927,8 +927,42 @@
       The following Key Idea gives conversions to/from our three spatial coordinate systems.
     </p>
 
-    <insight xml:id="idea_convert_coords" hstretch="330" hskip="45">
-    <!-- <insight xml:id="idea_convert_coords" hstretch="330"> -->
+    <insight xml:id="idea_convert_coords" hstretch="330" component="taypoly-early">
+      <title>Converting Between Rectangular, Cylindrical and Spherical Coordinates</title>
+      <p>
+        <ul>
+          <li>
+            <title>Rectangular and Cylindrical</title>
+            <p>
+              <md>
+                <mrow>\amp r^2 = x^2+y^2, \amp \amp \tan(\theta) = y/x,\amp  z\amp=z</mrow>
+                <mrow>\amp x=r\cos(\theta), \amp \amp y =r\sin(\theta),\amp  z\amp =z</mrow>
+              </md>
+            </p>
+          </li>
+          <li>
+            <title>Rectangular and Spherical</title>
+            <p>
+              <md>
+                <mrow>\amp \rho = \sqrt{x^2+y^2+z^2}, \amp \amp \tan(\theta) = y/x, \amp \amp \sin(\varphi) = z/\sqrt{x^2+y^2+z^2}</mrow>
+                <mrow>\amp x=\rho\cos(\varphi)\cos(\theta),\amp \amp y=\rho\cos(\varphi)\sin(\theta),\amp \amp z=\rho\sin(\varphi)</mrow>
+              </md>
+            </p>
+          </li>
+          <li>
+            <title>Cylindrical and Spherical </title>
+            <p>
+              <md>
+                <mrow>\amp \rho =\sqrt{r^2+z^2},\amp \amp  \theta = \theta,\amp \amp \tan(\varphi) = z/r</mrow>
+                <mrow>\amp r=\rho \cos(\varphi),\amp \amp  \theta = \theta,\amp \amp z=\rho\sin(\varphi)</mrow>
+              </md>
+            </p>
+          </li>
+        </ul>
+      </p>
+    </insight>
+
+    <insight xml:id="idea_convert_coords" hstretch="330" hskip="45" component="taypoly-late">
       <title>Converting Between Rectangular, Cylindrical and Spherical Coordinates</title>
       <p>
         <ul>
diff --git a/ptx/sec_double_int_volume.ptx b/ptx/sec_double_int_volume.ptx
index c8caa44ee..a2de4cef3 100644
--- a/ptx/sec_double_int_volume.ptx
+++ b/ptx/sec_double_int_volume.ptx
@@ -1012,7 +1012,7 @@
     </statement>
   </theorem>
 
-  <figure xml:id="vid-multint-double-general-region" component="video" vshift="11">
+  <figure xml:id="vid-multint-double-general-region" component="video" vshift="13">
     <caption>Evaluating a double integral over a more general region</caption>
     <video youtube="FcxnuFSNOfY" label="vid-multint-double-general-region"/>
   </figure>
diff --git a/ptx/sec_line_int_vf.ptx b/ptx/sec_line_int_vf.ptx
index be19afe22..0000709ca 100644
--- a/ptx/sec_line_int_vf.ptx
+++ b/ptx/sec_line_int_vf.ptx
@@ -1463,11 +1463,6 @@
       </solution>
     </example>
 
-    <figure xml:id="vid-veccalc-lineint-ftc-examples" component="video" vshift="0">
-      <caption>Further examples with the Fundamental Theorem (4 videos)</caption>
-      <video youtube="urwjnm5PXhQ" label="vid-veccalc-lineint-ftc-examples"/>
-    </figure>
-
     <p>
       The Fundamental Theorem of Line Integrals states that we can determine whether or not <m>\vec F</m> is conservative by determining whether or not <m>\vec F</m> has a potential function.
       This can be difficult.
@@ -1477,6 +1472,11 @@
       We state this simpler method as a theorem.
     </p>
 
+    <figure xml:id="vid-veccalc-lineint-ftc-examples" component="video" vshift="0">
+      <caption>Further examples with the Fundamental Theorem (4 videos)</caption>
+      <video youtube="urwjnm5PXhQ" label="vid-veccalc-lineint-ftc-examples"/>
+    </figure>
+
     <theorem xml:id="thm_conservative_field_curl">
       <title>Curl of Conservative Fields</title>
       <statement>
diff --git a/ptx/sec_multi_chain.ptx b/ptx/sec_multi_chain.ptx
index be39acc87..2c009e2ee 100644
--- a/ptx/sec_multi_chain.ptx
+++ b/ptx/sec_multi_chain.ptx
@@ -503,6 +503,11 @@
       </solution>
     </example>
 
+    <figure xml:id="vid-multi-chain-general" component="video-early" vshift="0">
+      <caption>Illustrating the chain rule, and interpreting as matrix multiplication (see <xref ref="sec_deriv_matrix"/>)</caption>
+      <video youtube="7jtaSujep7g" label="vid-multi-chain-general"/>
+    </figure>
+
     <example xml:id="ex_mchain4">
       <title>Using the Multivariable Chain Rule, Part II</title>
       <statement>
@@ -539,11 +544,6 @@
         </p>
       </solution>
     </example>
-
-    <!-- <figure xml:id="vid-multi-chain-general" component="video">
-      <caption>Illustrating the chain rule, and interpreting as matrix multiplication (see <xref ref="sec_deriv_matrix"/>)</caption>
-      <video youtube="7jtaSujep7g" label="vid-multi-chain-general"/>
-    </figure> -->
   </subsection>
 
   <subsection xml:id="subsec-implicit-diff">
diff --git a/ptx/sec_planes.ptx b/ptx/sec_planes.ptx
index 82578d290..afe81794b 100644
--- a/ptx/sec_planes.ptx
+++ b/ptx/sec_planes.ptx
@@ -301,7 +301,7 @@
           <!-- figures/figplanes1_3D.asy END -->
         </figure>
       </solution>
-      <solution component="video" vshift="6">
+      <solution component="video" vshift="7">
         <title>Video solution</title>
         <video width="98%" youtube="oc77R0am1vk" label="vid-vectors-planes-3points" component="video"/>
       </solution>
@@ -373,7 +373,7 @@
           it is sketched in <xref ref="fig_planes2"/>.
         </p>
 
-        <figure xml:id="fig_planes2" vshift="3">
+        <figure xml:id="fig_planes2" vshift="2.5">
           <caption>Sketching the plane in <xref ref="ex_planes2"/></caption>
 
           <!-- START figures/figplanes2_3D.asy -->
@@ -465,7 +465,7 @@
           The line and plane are sketched in <xref ref="fig_planes3"/>.
         </p>
 
-        <figure xml:id="fig_planes3" vshift="-1">
+        <figure xml:id="fig_planes3" vshift="1">
           <caption>The line and plane in <xref ref="ex_planes3"/></caption>
 
           <!-- START figures/figplanes3_3D.asy -->
@@ -530,7 +530,7 @@
           <!-- figures/figplanes3_3D.asy END -->
         </figure>
       </solution>
-      <solution component="video" vshift="4">
+      <solution component="video" vshift="-5">
         <title>Video solution</title>
         <video width="98%" youtube="2diP-H-QLoI" label="vid-vectors-planes-given-normal" component="video"/>
       </solution>
diff --git a/ptx/sec_ratio_root_tests.ptx b/ptx/sec_ratio_root_tests.ptx
index 4c542b3a4..1609ece38 100644
--- a/ptx/sec_ratio_root_tests.ptx
+++ b/ptx/sec_ratio_root_tests.ptx
@@ -269,6 +269,11 @@
       and does not work well with terms containing factorials.
     </p>
 
+    <figure xml:id="vid-seqseries-ratroot-root-test" component="video" vshift="-1">
+      <caption>Video presentation of <xref ref="thm_root_test"/></caption>
+      <video youtube="foE1iRYTXpc" label="vid-seqseries-ratroot-root-test"/>
+    </figure>
+
     <theorem xml:id="thm_root_test">
       <title>Root Test</title>
       <statement>
@@ -308,11 +313,6 @@
       </statement>
     </theorem>
 
-    <figure xml:id="vid-seqseries-ratroot-root-test" component="video" vshift="-1">
-      <caption>Video presentation of <xref ref="thm_root_test"/></caption>
-      <video youtube="foE1iRYTXpc" label="vid-seqseries-ratroot-root-test"/>
-    </figure>
-
     <example xml:id="ex_root1">
       <title>Applying the Root Test</title>
       <statement>
diff --git a/ptx/sec_space_coord.ptx b/ptx/sec_space_coord.ptx
index f77920f3c..44250e449 100644
--- a/ptx/sec_space_coord.ptx
+++ b/ptx/sec_space_coord.ptx
@@ -684,7 +684,7 @@
           and is bounded by planes in the <m>y</m> direction.
         </p>
 
-        <figure xml:id="fig_space3" vshift="-1">
+        <figure xml:id="fig_space3" vshift="0">
           <caption>Sketching the boundaries of a region in <xref ref="ex_space3"/></caption>
           <!-- START figures/figspace3_3D.asy -->
           <image width="47%">
@@ -746,7 +746,7 @@
           <!-- figures/figspace3_3D.asy END -->
         </figure>
       </solution>
-      <solution component="video" vshift="6">
+      <solution component="video" vshift="-6">
         <title>Video solution</title>
         <video width="98%" youtube="-9luj-GlMqA" label="vid-vectors-spacecoord-planes-eg" component="video"/>
       </solution>
diff --git a/ptx/sec_taylor_poly.ptx b/ptx/sec_taylor_poly.ptx
index 035a6e9aa..b10362835 100644
--- a/ptx/sec_taylor_poly.ptx
+++ b/ptx/sec_taylor_poly.ptx
@@ -1672,7 +1672,7 @@
                 </tabular> -->
               </figure>
 
-              <figure xml:id="fig_taypoly5a-early" vshift="-3.5" component="taypoly-early">
+              <figure xml:id="fig_taypoly5a-early" vshift="-3" component="taypoly-early">
                 <caption>A table of the derivatives of <m>f(x)=\sqrt{x}</m> evaluated at <m>x=4</m></caption>
                 <sidebyside>
                   <p>
diff --git a/ptx/sec_taylor_series.ptx b/ptx/sec_taylor_series.ptx
index b1d8e14fd..6fb0ffbf8 100644
--- a/ptx/sec_taylor_series.ptx
+++ b/ptx/sec_taylor_series.ptx
@@ -729,7 +729,7 @@
 
   <aside vshift="-4">
     <p>
-      Note that we require <m>h(x)</m> to be a polynomial function in <xref ref="thm_series_alg"/>.
+      Note that in <xref ref="thm_series_alg"/> we require <m>h(x)</m> to be a polynomial function.
       If we plug a function that is not polynomial into a power series,
       the result will no longer be a power series.
       If one is <em>very</em> careful about the center and radius of convergence,
diff --git a/ptx/sec_trigint.ptx b/ptx/sec_trigint.ptx
index 74d1c8129..3ecc1a181 100644
--- a/ptx/sec_trigint.ptx
+++ b/ptx/sec_trigint.ptx
@@ -784,18 +784,20 @@
       </solution>
     </example>
 
-    <p xml:id="vidint-int-trig-ex-secant-power-reduction" component="video">
-      Integrals involving odd powers of <m>\sec(x)</m> (and nothing else)
-      are often among the more intimidating tasks for beginning calculus students.
-      However, larger odd powers are best handled not by doing the integral directly,
-      but by employing a <em>reduction forumula</em>.
-      The video in <xref ref="vid-int-trig-ex-secant-power-reduction"/> shows how to obtain a reduction formula for the integral of <m>\sec^{2k+1}(x)</m>;
-      this formula allows us to express the integral in terms of an integral where the power of <m>\sec(x)</m>
-      is reduced by two.
-      <idx><h>reduction formula</h><h>trigonometric integral</h></idx>
-    </p>
+    <aside xml:id="vidint-int-trig-ex-secant-power-reduction" component="video" vshift="-3">
+      <p>
+        Integrals involving odd powers of <m>\sec(x)</m> (and nothing else)
+        are often among the more intimidating tasks for beginning calculus students.
+        However, larger odd powers are best handled not by doing the integral directly,
+        but by employing a <em>reduction forumula</em>.
+        The video in <xref ref="vid-int-trig-ex-secant-power-reduction"/> shows how to obtain a reduction formula for the integral of <m>\sec^{2k+1}(x)</m>;
+        this formula allows us to express the integral in terms of an integral where the power of <m>\sec(x)</m>
+        is reduced by two.
+        <idx><h>reduction formula</h><h>trigonometric integral</h></idx>
+      </p>
+    </aside>
 
-    <figure xml:id="vid-int-trig-ex-secant-power-reduction" component="video" vshift="-1">
+    <figure xml:id="vid-int-trig-ex-secant-power-reduction" component="video" vshift="-7">
       <caption>Deriving a power reduction formula for secant integrals</caption>
       <video youtube="Om0iOgV9IwA" label="vid-int-trig-ex-secant-power-reduction"/>
     </figure>
diff --git a/ptx/sec_triple_int.ptx b/ptx/sec_triple_int.ptx
index 56edeade2..d794a35ee 100644
--- a/ptx/sec_triple_int.ptx
+++ b/ptx/sec_triple_int.ptx
@@ -2877,7 +2877,31 @@
 
     <!-- <pagebreak-latex/> -->
     
-    <definition xml:id="def_triple_integral_2" hstretch="360" hskip="70">
+    <definition xml:id="def_triple_integral_2" hstretch="360" hskip="70" component="taypoly-late">
+      <title>Iterated Integration, (Part II)</title>
+      <statement>
+        <p>
+          Let <m>D</m> be a closed,
+          bounded region in space,
+          over which <m>g_1(x)</m>, <m>g_2(x)</m>, <m>f_1(x,y)</m>,
+          <m>f_2(x,y)</m> and <m>h(x,y,z)</m> are all continuous,
+          and let <m>a</m> and <m>b</m> be real numbers.
+        </p>
+
+        <p>
+          The <term>iterated integral</term>
+          <m>\ds \int_a^b\int_{g_1(x)}^{g_2(x)}\int_{f_1(x,y)}^{f_2(x,y)} h(x,y,z)\, dz\, dy\, dx</m> is evaluated as
+              <idx><h>integration</h><h>triple</h></idx>
+              <idx><h>triple integral</h></idx>
+              <idx><h>iterated integration</h></idx>
+          <md>
+            \int_a^b\int_{g_1(x)}^{g_2(x)}\int_{f_1(x,y)}^{f_2(x,y)} h(x,y,z)\, dz\, dy\, dx = \int_a^b\int_{g_1(x)}^{g_2(x)}\left(\int_{f_1(x,y)}^{f_2(x,y)} h(x,y,z)\, dz\right) dy\, dx
+          </md>.
+        </p>
+      </statement>
+    </definition>
+
+    <definition xml:id="def_triple_integral_2" hstretch="360" component="taypoly-early">
       <title>Iterated Integration, (Part II)</title>
       <statement>
         <p>