APEXCalculus · sean-fitzpatrick · Jun 29, 2026 · Jul 6, 2026 · Jul 6, 2026 · Jul 6, 2026
diff --git a/.devcontainer/devcontainer.json b/.devcontainer/devcontainer.json
@@ -15,7 +15,7 @@
 {
   "image": "pretextbook/pretext-full:latest", // uses latest image from https://hub.docker.com/r/PreTeXtBook/pretext-full/tags
   // If you don't need sagemath, you can use a smaller base image.  Comment out the line above and uncomment the line below to use a smaller image.
-  // "image": "pretextbook/pretext:1.10",
+  // "image": "pretextbook/pretext:1.11",
   "features": {"ghcr.io/devcontainers/features/github-cli": {}},
 
   // The pretext-full image above includes pretext, prefigure, and enough parts of latex and sagemath for most cases.  Here we install additional dependencies.

diff --git a/ptx/appendix_back_reference.ptx b/ptx/appendix_back_reference.ptx
@@ -513,14 +513,14 @@
               <cell><m>\cos(\theta) = x</m></cell>
             </row>
             <row>
-              <cell/>
+              <cell/><cell/>
             </row>
             <row>
               <cell><m>\ds\csc(\theta) = \frac1y</m></cell>
               <cell><m>\ds\sec(\theta) = \frac1x</m></cell>
             </row>
             <row>
-              <cell/>
+              <cell/><cell/>
             </row>
             <row>
               <cell><m>\ds\tan(\theta) = \frac yx</m></cell>
@@ -564,14 +564,14 @@
               <cell><m>\ds\csc(\theta) = \frac{\text{H} }{\text{O} }</m></cell>
             </row>
             <row>
-              <cell/>
+              <cell/><cell/>
             </row>
             <row>
               <cell><m>\ds\cos(\theta) = \frac{\text{A} }{\text{H} }</m></cell>
               <cell><m>\ds\sec(\theta) = \frac{\text{H} }{\text{A} }</m></cell>
             </row>
             <row>
-              <cell/>
+              <cell/><cell/>
             </row>
             <row>
               <cell><m>\ds\tan(\theta) = \frac{\text{O} }{\text{A} }</m></cell>

diff --git a/ptx/review-exercises-limits.ptx b/ptx/review-exercises-limits.ptx
@@ -272,7 +272,7 @@
               For a numerical approximation, make a table:
             </p>
             <tabular>
-              <row bottom="medium">
+              <row bottom="minor">
                 <cell><m>x</m></cell>
                 <cell><m>
                   <var name="$f"/>

diff --git a/ptx/sec_ABC.ptx b/ptx/sec_ABC.ptx
diff --git a/ptx/sec_arc_length.ptx b/ptx/sec_arc_length.ptx
diff --git a/ptx/sec_conic_sections.ptx b/ptx/sec_conic_sections.ptx
@@ -1540,7 +1540,7 @@
             <caption>Graphing the hyperbola in <xref ref="ex_conic5"/></caption>
             <!-- START figures/fig_conic5.tex -->
             <image width="47%">
-              <shortdescription>A graph of the hyperbola given in <xref ref="ex_conic5"/></shortdescription>
+              <shortdescription>A graph of the hyperbola in this example</shortdescription>
               <description>
                 <p>
                  A graph of the hyperbola given in <xref ref="ex_conic5"/>.
@@ -1627,7 +1627,7 @@
             <caption>Graphing the hyperbola in <xref ref="ex_conic6"/></caption>
             <!-- START figures/fig_conic6.tex -->
             <image width="47%">
-              <shortdescription>The hyperbola described in <xref ref="ex_conic6"/>.</shortdescription>
+              <shortdescription>The hyperbola described in this example</shortdescription>
               <description>
                 <p>
                   The hyperbola described in  <xref ref="ex_conic6"/>.
@@ -2124,7 +2124,7 @@
           <figure xml:id="fig_hyperbola_locateb">
             <caption/>
             <image>
-              <shortdescription>A hyperbola drawn from points A and B in <xref ref="fig_hyperbola_locatea"/> </shortdescription>
+              <shortdescription>A hyperbola drawn from points A and B to illustrate the location property </shortdescription>
               <description>
                 <p>
                   A hyperbola drawn from points <m>A</m> and <m>B</m> in <xref ref="fig_hyperbola_locatea"/>.
@@ -2161,7 +2161,7 @@
           <figure xml:id="fig_hyperbola_locatec">
             <caption/>
             <image>
-              <shortdescription>A fourth point found from hyperbolas given by points in <xref ref="fig_hyperbola_locatea"/></shortdescription>
+              <shortdescription>A fourth point found from hyperbolas given by points in the previous figures</shortdescription>
               <description>
                 <p>
                   A hyperbola drawn from points <m>B</m> and <m>C</m> in <xref ref="fig_hyperbola_locatea"/>, intersecting with the hyperbola drawn in <xref ref="fig_hyperbola_locateb"/>.

diff --git a/ptx/sec_def_int.ptx b/ptx/sec_def_int.ptx
@@ -983,8 +983,10 @@
               The graph area under the curve is a semicircle with radius 3 on the x axis with centre at origin.
             </shortdescription>
             <description>
-              The graph shows the area under the curve that is a semicircle with radius <m>3</m> on the <m>x</m> axis
-              with centre at origin. It lies on the first and the second quadrant.
+              <p>
+                The graph shows the area under the curve that is a semicircle with radius <m>3</m> on the <m>x</m> axis
+                with centre at origin. It lies on the first and the second quadrant.
+              </p>
             </description>
 
             <latex-image label="img_defint8b">
@@ -1658,16 +1660,16 @@
                 <image>
                   <shortdescription>
                     Graph of function that is a semicircle on the x axis.
-                    </shortdescription>
-                    <description>
+                  </shortdescription>
+                  <description>
                     <p>
-                    The <m>y</m> axis is drawn from <m>0</m> to <m>3</m> and the <m>x</m> axis is
-                    drawn from <m>0</m> to <m>4</m>.
-                    The graph of function <m>f(x) = \sqrt{4-(x-2)^2}</m>
-                    is a semi circle drawn on the <m>x</m> axis with centre at point
-                    <m>(2,0)</m> and radius of <m>2</m>.
+                      The <m>y</m> axis is drawn from <m>0</m> to <m>3</m> and the <m>x</m> axis is
+                      drawn from <m>0</m> to <m>4</m>.
+                      The graph of function <m>f(x) = \sqrt{4-(x-2)^2}</m>
+                      is a semi circle drawn on the <m>x</m> axis with centre at point
+                      <m>(2,0)</m> and radius of <m>2</m>.
                     </p>
-                    </description>
+                  </description>
 
                   <latex-image label="img_05_02_ex_09">
                     \begin{tikzpicture}

diff --git a/ptx/sec_deriv_basic_rules.ptx b/ptx/sec_deriv_basic_rules.ptx
@@ -812,7 +812,7 @@
                <fillin width="25" answer="the power rule"/>
             </p>
           </statement>
-          <evaluation component="web">
+          <evaluation>
             <evaluate>
 
               <test correct="yes">

diff --git a/ptx/sec_deriv_chainrule.ptx b/ptx/sec_deriv_chainrule.ptx
@@ -1079,11 +1079,13 @@
           3 gears of various sizes demonstrating the chain rule.
         </shortdescription>
         <description>
-          Three gears, connected in the order <m>x,u,y</m>.
-          <m>x</m> is the largest gear, having 36 teeth. It is rotating counter-clockwise.
-          <m>u</m> is connected to <m>x</m>, and it has 18 teeth. To the left of the connection is <m>\frac{du}{dx} = 2</m>.
-          <m>y</m> is connected to <m>u</m>, and it has 6 teeth. Below the connection is <m>\frac{dy}{du}=3</m>.
-          To the right of the gears is the expression <m>\frac{dy}{dx} = 6</m>.
+          <p>
+            Three gears, connected in the order <m>x,u,y</m>.
+            <m>x</m> is the largest gear, having 36 teeth. It is rotating counter-clockwise.
+            <m>u</m> is connected to <m>x</m>, and it has 18 teeth. To the left of the connection is <m>\frac{du}{dx} = 2</m>.
+            <m>y</m> is connected to <m>u</m>, and it has 6 teeth. Below the connection is <m>\frac{dy}{du}=3</m>.
+            To the right of the gears is the expression <m>\frac{dy}{dx} = 6</m>.
+          </p>
         </description>
         <latex-image label="img_chainrulegears">
 

diff --git a/ptx/sec_deriv_implicit.ptx b/ptx/sec_deriv_implicit.ptx
@@ -426,16 +426,18 @@
               A curve with two distinct segments and a tangent line with a positive slope
             </shortdescription>
             <description>
-              Two curves are drawn in the <m>xy</m>-plane.
-              The left curve stretches upwards from the left side of the <m>y</m> axis, curving slightly to the left.
-              As <m>y</m> approaches -2, the curve begins to widen to the left, creating a bump in the curve.
-              As the curve crosses the <m>x</m> axis, the curve moves towards the right, no longer increasing and becoming more horizontal as <m>x</m> increases.
-              At the point <m>(0,1)</m>, a tangent line is drawn, with a moderate positive slope.
-              This point corresponds to the corner at which the curve begins to become horizontal.
-              At this point, the curve passes the vertical line test, but does not at most other points on the graph.
-              The second curve begins to the right of the <m>y</m>-axis, as a line stretching upwards from the bottom of the <m>y</m>-axis.
-              As <m>x</m> approaches 1, the curve also begins to become horizontal as <m>x</m> increases.
-              The entire second curve lies in the fourth quadrant.
+              <p>
+                Two curves are drawn in the <m>xy</m>-plane.
+                The left curve stretches upwards from the left side of the <m>y</m> axis, curving slightly to the left.
+                As <m>y</m> approaches -2, the curve begins to widen to the left, creating a bump in the curve.
+                As the curve crosses the <m>x</m> axis, the curve moves towards the right, no longer increasing and becoming more horizontal as <m>x</m> increases.
+                At the point <m>(0,1)</m>, a tangent line is drawn, with a moderate positive slope.
+                This point corresponds to the corner at which the curve begins to become horizontal.
+                At this point, the curve passes the vertical line test, but does not at most other points on the graph.
+                The second curve begins to the right of the <m>y</m>-axis, as a line stretching upwards from the bottom of the <m>y</m>-axis.
+                As <m>x</m> approaches 1, the curve also begins to become horizontal as <m>x</m> increases.
+                The entire second curve lies in the fourth quadrant.
+              </p>
             </description>
             <latex-image label="img_implicit4">
 
@@ -1995,9 +1997,11 @@
                   A square with rounded corners and edges with a point in the first quadrant.
                 </shortdescription>
                 <description>
-                  A curve that lies in all 4 quadrants.
-                  It has the appearance of a square with rounded sides and corners.
-                  A point is drawn at <m>(\sqrt{0.6},\sqrt{0.8})</m>.
+                  <p>
+                    A curve that lies in all 4 quadrants.
+                    It has the appearance of a square with rounded sides and corners.
+                    A point is drawn at <m>(\sqrt{0.6},\sqrt{0.8})</m>.
+                  </p>
                 </description>
                 <latex-image label="img_02_06_ex_28">
                   \begin{tikzpicture}
@@ -2126,16 +2130,18 @@
                   An oval with a cusp on the right side.
                 </shortdescription>
                 <description>
-                  An oval with a cusp on the right side.
-                  A majority of the curve lies to the left of the <m>y</m>-axis.
-                  From the top of the curve, the curve decreases towards the right.
-                  It enters the first quadrant through the point <m>(0,1)</m>.
-                  As the curve nears the <m>x</m>-axis, it bends back toward the <m>y</m>-axis, forming a cusp at the origin.
-                  The curve then bends outwards into the fourth quadrant.
-                  The curve continues downwards and to the left, passing the <m>y</m>-axis through the point <m>(0,-1)</m>.
-                  In the third quadrant the curve bends upwards, passing vertically into the second quadrant through the point <m>(-2,0)</m>.
-                  The curve bends upwards and to the right, once again meeting the top of the curve.
-                  The point at the top of the curve is drawn at <m>(-\frac{3}{4},\frac{3\sqrt{3}}{4})</m>.
+                  <p>
+                    An oval with a cusp on the right side.
+                    A majority of the curve lies to the left of the <m>y</m>-axis.
+                    From the top of the curve, the curve decreases towards the right.
+                    It enters the first quadrant through the point <m>(0,1)</m>.
+                    As the curve nears the <m>x</m>-axis, it bends back toward the <m>y</m>-axis, forming a cusp at the origin.
+                    The curve then bends outwards into the fourth quadrant.
+                    The curve continues downwards and to the left, passing the <m>y</m>-axis through the point <m>(0,-1)</m>.
+                    In the third quadrant the curve bends upwards, passing vertically into the second quadrant through the point <m>(-2,0)</m>.
+                    The curve bends upwards and to the right, once again meeting the top of the curve.
+                    The point at the top of the curve is drawn at <m>(-\frac{3}{4},\frac{3\sqrt{3}}{4})</m>.
+                  </p>
                 </description>
                 <latex-image label="img_02_06_ex_30">
                   \begin{tikzpicture}

diff --git a/ptx/sec_deriv_intro.ptx b/ptx/sec_deriv_intro.ptx
@@ -795,13 +795,20 @@
           </md>.
         </p>
 
-        <p>
+        <p component="novideo">
           Thus our approximation of the equation of the tangent line is
           <m>y = 0.9983(x-0) +0 = 0.9983x</m>;
           it is graphed in <xref ref="fig_tangentsinx"/>.
           The graph seems to imply the approximation is rather good.
         </p>
 
+        <p component="video">
+          Thus our approximation of the equation of the tangent line is
+          <m>y = 0.9983(x-0) +0 = 0.9983x</m>;
+          it is graphed in <xref ref="fig_tangentsinx-vid"/>.
+          The graph seems to imply the approximation is rather good.
+        </p>
+
         <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 -->
@@ -839,7 +846,7 @@
           </image>
           <!-- figures/fig_tangentsinx.tex END -->
         </figure>
-        <figure xml:id="fig_tangentsinx" vshift="-1" component="video">
+        <figure xml:id="fig_tangentsinx-vid" 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_prodquot.ptx b/ptx/sec_deriv_prodquot.ptx
@@ -918,7 +918,7 @@
               <fillin width="30" answer="the quotient rule"/>
             </p>
           </statement>
-          <evaluation component="web">
+          <evaluation>
             <evaluate>
 
               <test correct="yes">

diff --git a/ptx/sec_directional_derivative.ptx b/ptx/sec_directional_derivative.ptx
@@ -1304,7 +1304,7 @@
             <evaluation>
               <evaluate>
                 <test correct="yes">
-                  <strcmp usee-answer="yes" case="insensitive"/>
+                  <strcmp use-answer="yes" case="insensitive"/>
                 </test>
                 <test>
                   <strcmp case="insensitive">perpendicular</strcmp>

diff --git a/ptx/sec_graph_incr_decr.ptx b/ptx/sec_graph_incr_decr.ptx
@@ -544,6 +544,7 @@
 
         <!-- START figures/fig_incrline1.tex -->
         <image width="47%">
+          <shortdescription>A number line showing the two critical points for a function</shortdescription>
           <description>
             <p>
               A number line is shown with two marked points.
@@ -1256,7 +1257,22 @@
         <caption>A graph of <m>f(x)</m> in <xref ref="ex_incr3"/>, showing where <m>f</m> is increasing and decreasing</caption>
         <!-- START figures/fig_incr3.tex -->
         <image width="47%">
-          <description/>
+          <shortdescription>A graph with a curved W shape.</shortdescription>
+          <description>
+            <p>
+              The graph of the function <m>f(x)</m> in <xref ref="ex_incr3"/> is plotted,
+              along with its derivative.
+              The graph of <m>f(x)</m> has the shape of a curved W.
+              There are two local minima with horizontal tangent lines at <m>x=1</m> and <m>x=-1</m>.
+              There is a local maximum that is a cusp at the origin.
+            </p>
+            <p>
+              The graph of <m>\fp(x)</m> is shown to be decreasing when <m>x</m> is negative,
+              with an intercept at <m>x=-1</m>. There is a break in the graph at the <m>y</m> axis,
+              since the derivative is undefined there.
+              For positive <m>x</m>, the graph of <m>\fp(x)</m> is increasing, with an intercept at <m>x=1</m>.
+            </p>
+          </description>  
           <latex-image label="img_incr3">
             \begin{tikzpicture}
               \begin{axis}[

diff --git a/ptx/sec_graph_sketch.ptx b/ptx/sec_graph_sketch.ptx
@@ -1113,7 +1113,7 @@
       <figure>
         <caption><pubtitle>Sage</pubtitle> output</caption>
         <image xml:id="img_sage_sinx" source="images/img_sage_sinx">
-          <shortdescription> A graph of <m>y = \sin(x)</m> generated by Sage. </shortdescription>
+          <shortdescription> A graph of the sine function generated by Sage. </shortdescription>
           <description>
             <p>
               The plot features a solid blue curve representing the sine wave.

diff --git a/ptx/sec_hyperbolic.ptx b/ptx/sec_hyperbolic.ptx
@@ -909,8 +909,8 @@
                 The <m>y</m> and the <m>x</m> axes are drawn from <m>-10</m> to
                 <m>10</m>. The functions <m>y=\sinh(x)</m> and <m>y=\sinh^{-1}(x)</m>.
                 The axis <m>y=x</m> is shown.
-              <p>
               </p>
+              <p>
                 From left to right, the <m>\sinh(x)</m> function starts in the third
                 quadrant and it rises steeply, very closely to the <m>y</m> axis. It
                 crosses the origin along the <m>y=x</m> line, has a dip then increases

diff --git a/ptx/sec_limit_continuity.ptx b/ptx/sec_limit_continuity.ptx
@@ -1496,7 +1496,7 @@
               <cell/>
             </row>
             <row>
-              <cell/>
+              <cell/><cell/><cell/>
             </row>
           </tabular>
 
@@ -3274,7 +3274,7 @@
               <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 component="web">
-                <row bottom="medium">
+                <row bottom="minor">
                   <cell>Iteration</cell>
                   <cell>Interval</cell>
                   <cell>Midpoint Sign</cell>
@@ -3364,7 +3364,7 @@
               <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 component="web">
-                <row bottom="medium">
+                <row bottom="minor">
                   <cell>Iteration</cell>
                   <cell>Interval</cell>
                   <cell>Midpoint Sign</cell>
@@ -3454,7 +3454,7 @@
               <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 component="web">
-                <row bottom="medium">
+                <row bottom="minor">
                   <cell>Iteration</cell>
                   <cell>Interval</cell>
                   <cell>Midpoint Sign</cell>
@@ -3544,7 +3544,7 @@
               <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 component="web">
-                <row bottom="medium">
+                <row bottom="minor">
                   <cell>Iteration</cell>
                   <cell>Interval</cell>
                   <cell>Midpoint Sign</cell>