remove permid tags

source/calculus/source/02-DF/04.ptx

@@ -14,7 +14,7 @@
 
     <activity xml:id="activity-df-product-rule-intro">
       <introduction>
-        <p permid="TEn"> Let <m>f</m> and <m>g</m> be the functions defined by <me>f(t) = 2t^2 \, ,
+        <p> Let <m>f</m> and <m>g</m> be the functions defined by <me>f(t) = 2t^2 \, ,
           \, g(t) = t^3 + 4t. </me>
         </p>
       </introduction>
@@ -139,7 +139,7 @@
 
 <activity xml:id="activity-df-quotient-rule-intro">
  <introduction>
-     <p permid="TEn">
+     <p>
     Let <m>f</m> and <m>g</m> be the functions defined by
            <me>f(t) = 2t^2 \, , \, g(t) = t^3 + 4t.</me>
      </p>

source/calculus/source/03-AD/03.ptx

@@ -276,7 +276,7 @@ recall that when <m>y</m> is a function of <m>x</m>, which in turn is a function
 
 
 <!-- More variables here. Requires solving for h in terms of r. -->
-<activity xml:id="rel-rates-conical-tank" permid="DEn">
+<activity xml:id="rel-rates-conical-tank">
   <introduction>
     <p>
       A water tank has the shape of an inverted circular cone (the cone points downwards) with a base of radius 6 feet and a depth of 8 feet. Suppose that water is being pumped into the tank at a constant instantaneous rate of 4 cubic feet per minute.

source/calculus/source/03-AD/06.ptx

@@ -121,7 +121,7 @@
       <p>
         Sketch a sequence of tangent lines at various points to each of the following curves in <xref ref="concavity-2"/>. 
       </p>
-          <figure xml:id="concavity-2" permid="PJf">
+          <figure xml:id="concavity-2">
       <caption>From left to right, three functions that are all decreasing.</caption>
       <sidebyside widths="30% 30% 30%">
         <image>
@@ -193,7 +193,7 @@
 
 
 <remark xml:id="activity-remark-concavity-terminology"><p>Recall the terminology of concavity: when a curve bends upward, we say its shape is concave up. When a curve bends downwards, we say its shape is concave down.</p></remark>
-<!--     <p permid="KZm">
+<!--     <p>
       We now introduce the notion of <em>concavity</em>
           <idx><h>concavity</h></idx>
       which provides simpler language to describe these behaviors.
@@ -211,7 +211,7 @@
     <activity xml:id="activity-derivative-concavity3a">
     <statement><p>Look at the curves in <xref ref="concavity-3"/>. Which curve is concave up? Which one is concave down? Why? Try to explain using the graph!</p>
 
-        <figure xml:id="concavity-3" permid="vQo">
+        <figure xml:id="concavity-3">
         <caption>Two concavities, which is which? </caption>
         <sidebyside widths="45% 45%">
             <image>
@@ -236,9 +236,9 @@
     </answer>
     </activity>
 
-    <definition xml:id="concavity-and-first-derivative" permid="hcP">
+    <definition xml:id="concavity-and-first-derivative">
       <statement>
-        <p permid="slO">
+        <p >
           Let <m>f</m> be a differentiable function on some interval <m>(a,b)</m>.
           Then <m>f</m> is <term>concave up</term>
               <idx><h>concave up</h></idx>

source/calculus/source/03-AD/08.ptx

@@ -175,8 +175,8 @@
             </p>
           </li>
 
-          <li permid="vol">
-            <p permid="stF">
+          <li>
+            <p>
               Determine a <em>function of a single variable</em> that models the quantity to be optimized;
               this may involve using other relationships among variables to eliminate one or more variables in the function formula.
               For example, in <xref ref="activity-ad8-box"/>,
@@ -187,16 +187,16 @@
             </p>
           </li>
 
-          <li permid="bvu">
-            <p permid="YAO">
+          <li>
+            <p>
               Decide the <em>domain</em> on which to consider the function being optimized.
               Often the physical constraints of the problem will limit the possible values that the independent variable can take on.
               Thinking back to the diagram describing the overall situation and any relationships among variables in the problem often helps identify the smallest and largest values of the input variable.
             </p>
           </li>
 
-          <li permid="HCD">
-            <p permid="EHX">
+          <li>
+            <p>
               <em>Use calculus</em> to identify the global maximum and/or minimum of the quantity being optimized.
               This always involves finding the critical numbers of the function first.
               Then, depending on the domain,
@@ -207,8 +207,8 @@
             </p>
           </li>
 
-          <li permid="nJM">
-            <p permid="kPg">
+          <li>
+            <p>
               Finally, we make certain we have <em>answered the question</em>:
              what are the optimal points and what optimal values do we obtain at these points? 
             </p>
@@ -233,7 +233,7 @@
         Label these quantities appropriately on the image shown in <xref ref="F-3-4-PA1">Figure</xref>.
       </p>
 
-      <figure xml:id="F-3-4-PA1" permid="RHW">
+      <figure xml:id="F-3-4-PA1">
         <caption>A rectangular parcel with a square end.</caption>
         <image>
           <prefigure xmlns="https://prefigure.org" label="prefigure-AD8-parcel1">

source/calculus/source/04-IN/02.ptx

@@ -13,20 +13,20 @@
     <title>Activities</title>
 
     <!--Preview Activity 4.1.1 from Active Calculus -->
- <activity xml:id="integration-riemann-1" permid="KNr">
+ <activity xml:id="integration-riemann-1" >
  <introduction>
-  <p permid="eGi">
+  <p>
     Suppose that a person is taking a walk along a long straight path and walks at a constant rate of 3 miles per hour.
     </p>
  </introduction>
 
-      <task permid="IYe">
-        <p permid="NHX">
+      <task>
+        <p>
           On the left-hand axes provided in <xref ref="F-4-2-IN1">Figure</xref>,
           sketch a labeled graph of the velocity function <m>v(t) = 3</m>.
         </p>
 
-        <figure xml:id="F-4-2-IN1" permid="ZWp">
+        <figure xml:id="F-4-2-IN1">
           <caption>At left,
           axes for plotting <m>y = v(t)</m>;
           at right, for plotting
@@ -45,53 +45,53 @@
           </sidebyside>
         </figure>
 
-        <p permid="tPg">
+        <p>
           Note that while the scale on the two sets of axes is the same,
           the units on the right-hand axes differ from those on the left.
           The right-hand axes will be used in question (d).
         </p>
       </task>
 
-      <task permid="pfn">
-        <p permid="Gdy">
+      <task>
+        <p>
           How far did the person travel during the two hours?
           How is this distance related to the area of a certain region under the graph of <m>y = v(t)</m>?
         </p>
       </task>
 
-      <task permid="Vmw">
-        <p permid="mkH">
+      <task>
+        <p>
           Find an algebraic formula, <m>s(t)</m>,
           for the position of the person at time <m>t</m>,
           assuming that <m>s(0) = 0</m>.
           Explain your thinking.
         </p>
       </task>
 
-      <task permid="BtF">
-        <p permid="SrQ">
+      <task>
+        <p>
           On the right-hand axes provided in <xref ref="F-4-2-IN1" />,
           sketch a labeled graph of the position function <m>y = s(t)</m>.
         </p>
       </task>
 
-      <task permid="hAO">
-        <p permid="yyZ">
+      <task>
+        <p>
           For what values of <m>t</m> is the position function <m>s</m> increasing?
           Explain why this is the case using relevant information about the velocity function <m>v</m>.
         </p>
       </task>
   </activity> 
 
-<activity xml:id="act-4-1-1" permid="gon">
+<activity xml:id="act-4-1-1">
   <introduction>
-    <p permid="WUB">
+    <p>
       Suppose that a person is walking in such a way that her velocity varies slightly according to the information given in 
       the table and graph below.
     </p>
 
-    <sidebyside widths="47% 47%" margins="auto" valign="middle" permid="nSM">
-      <tabular permid="HLD">
+    <sidebyside widths="47% 47%" margins="auto" valign="middle">
+      <tabular>
         <row bottom="minor" halign="center">
           <cell><m>t</m></cell>
           <cell><m>v(t)</m></cell>
@@ -141,8 +141,8 @@
     </sidebyside>
   </introduction>
 
-        <task permid="JWp">
-          <p permid="Ehd">
+        <task>
+          <p>
             Using the grid, graph,
             and given data appropriately,
             estimate the distance traveled by the walker during the two hour interval from <m>t = 0</m> to <m>t = 2</m>.
@@ -151,24 +151,24 @@
           </p>
         </task>
 
-        <task permid="qdy">
-          <p permid="kom">
+        <task>
+          <p>
             How could you get a better approximation of the distance traveled on <m>[0,2]</m>?
             Explain, and then find this new estimate.
           </p>
         </task>
 
-        <task permid="WkH">
-          <p permid="Qvv">
+        <task>
+          <p >
             Now suppose that you know that <m>v</m> is given by <m>v(t) = 0.5t^3-1.5t^2+1.5t+1.5</m>.
             Remember that <m>v</m> is the derivative of the walker's position function,
             <m>s</m>.
             Find a formula for <m>s</m> so that <m>s' = v</m>.
           </p>
         </task>
 
-        <task permid="CrQ">
-          <p permid="wCE">
+        <task >
+          <p >
             Based on your work in (c),
             what is the value of <m>s(2) - s(0)</m>?
             What is the meaning of this quantity?

source/calculus/source/04-IN/03.ptx

@@ -15,7 +15,7 @@
     <!--DEFINITION OF ANTIDERIVATIVE from Active Calculus -->
     <definition xml:id="def-antiderivative">
       <statement>
-        <p permid="ctJ">
+        <p>
           If <m>g</m> and <m>G</m> are functions such that <m>G' = g</m>,
           we say that <m>G</m> is an <term>antiderivative</term>
               <idx><h>antiderivative</h></idx>
@@ -72,12 +72,12 @@
 
        <remark>
 
-    <p permid="cfB">
+    <p>
       We now note that whenever we know the derivative of a function,
       we have a <em>function-derivative pair</em>,
       so we also know the antiderivative of a function.
       For instance, in <xref ref="elem-antider-intro"/> we could use our prior knowledge that 
-      <me permid="YfC">
+      <me>
         \frac{d}{dx}[\sin(x)] = \cos(x)
       </me>,
      to determine that <m>F(x) = \sin(x)</m> is an antiderivative of <m>f(x) = \cos(x)</m>.
@@ -87,24 +87,24 @@
     </p>
 
 
-      <p permid="MWD">
+      <p>
       In the following activity,
       we work to build a list of basic functions whose antiderivatives we already know.
     </p>  
     </remark>
 
-<activity xmlns:xi="http://www.w3.org/2001/XInclude" xml:id="act-4-4-2" permid="ovP">
+<activity xmlns:xi="http://www.w3.org/2001/XInclude" xml:id="act-4-4-2" >
   <statement>
-    <p permid="yUU">
+    <p>
       Use your knowledge of derivatives of basic functions to complete <xref ref="T-4-4-Act2">Table</xref> of antiderivatives.
       For each entry,
       your task is to find a function <m>F</m> whose derivative is the given function <m>f</m>.
 
     </p>
 
-    <table xml:id="T-4-4-Act2" permid="PTf">
+    <table xml:id="T-4-4-Act2">
       <title>Familiar basic functions and their antiderivatives.</title>
-      <tabular top="minor" bottom="minor" permid="wao">
+      <tabular top="minor" bottom="minor">
         <row bottom="medium">
           <cell>given function, <m>f(x)</m></cell>
           <cell>antiderivative, <m>F(x)</m>   <nbsp /></cell>
@@ -176,7 +176,7 @@
 
 <activity xml:id="act-antider-const-mult">
 
-  <introduction> <p permid="ImK">
+  <introduction> <p>
       In <xref ref="act-4-4-2">Activity</xref>,
       we constructed a list of the basic antiderivatives we know at this time.
       Those rules will help us  antidifferentiate sums and constant multiples of basic functions. For example,

source/calculus/source/04-IN/08.ptx

@@ -92,8 +92,8 @@
     </activity>    
 
 
-    <fact permid="LKt">
-      <p permid="BVi">
+    <fact>
+      <p>
         If two curves <m>y = f(x)</m> and
         <m>y = g(x)</m> intersect at <m>(a,g(a))</m> and <m>(b,g(b))</m>,
         and for all <m>x</m> such that

source/calculus/source/07-CO/04.ptx

@@ -14,7 +14,7 @@
 
     <fact xml:id="fact-CO4polar">
 
-      <p permid="QCd">
+      <p>
 
     <q>As the crow flies</q> is an idiom used to describe the most direct path between two points.
     The <term>polar coordinate system</term><idx>polar coordinate system</idx> is a useful parametrization of the plane that, rather than describing horizontal and vertical position relative to the origin in the usual way, describes a point in terms of distance from the origin and direction.
@@ -137,7 +137,7 @@ Graph each of the following.
 
     <fact xml:id="fact-CO4symmetryTestX">
 
-      <p permid="QCd">
+      <p>
         If a polar graph is symmetric about the <m>x</m>-axis, then if the point <m>(r,\theta)</m> lies on the graph, then the point <m>(r,-\theta)</m> or <m>(-r, \pi-\theta)</m> also lies on the graph.
 
       </p>
@@ -146,7 +146,7 @@ Graph each of the following.
 
     <fact xml:id="fact-CO4symmetryTestY">
 
-      <p permid="QCd">
+      <p>
         If a polar graph is symmetric about the <m>y</m>-axis, then if the point <m>(r,\theta)</m> lies on the graph, then the point <m>(r,\pi-\theta)</m> or <m>(-r,-\theta)</m> also lies on the graph.
 
       </p>
@@ -155,7 +155,7 @@ Graph each of the following.
 
     <fact xml:id="fact-CO4symmetryTestOrigin">
 
-      <p permid="QCd">
+      <p>
         If a polar graph is rotationally symmetric about the origin, then if the point <m>(r,\theta)</m> lies on the graph, then the point <m>(-r,\theta)</m> or <m>(r,\pi+\theta)</m> also lies on the graph.
 
       </p>
@@ -196,7 +196,7 @@ Find a Cartesian form of each of the given polar equations.
 
         <fact xml:id="fact-CO4slopePolarCurve">
 
-      <p permid="QCd">
+      <p >
         The slope of a polar curve <m>r=f(\theta)</m>is <m>\displaystyle\frac{dy}{dx}=\displaystyle\frac{dy/d\theta}{dx/d\theta}=\displaystyle\frac{f^\prime(\theta)\sin(\theta)+f(\theta)\cos(\theta)}{f^\prime(\theta)\cos(\theta)-f(\theta)\sin(\theta)}</m>, provided that <m>dx/d\theta\neq 0</m> at <m>(r,\theta)</m>.
           Vertical tangents occur when <m>dy/d\theta=0</m> and <m>dx/d\theta\neq 0</m>;
           horizontal tangents occur when <m>dx/d\theta=0</m> and <m>dy/d\theta\neq 0</m>.

source/calculus/source/07-CO/06.ptx

@@ -114,7 +114,7 @@
 
       <fact xml:id="fact-CO6polarIntegral">
 
-      <p permid="QCd">
+      <p >
         The area of the <q>fan-shaped</q> region between the pole and <m>r=f(\theta)</m> as the angle <m>\theta</m> ranges from <m>\alpha</m> to <m>\beta</m> is given by
           <me>\int_{\theta=\alpha}^{\theta=\beta} \frac{r^2}{2}d\theta</me>.