Latest build deployed.

course/index.html

@@ -2,7 +2,7 @@
 <html>
 <!--********************************************-->
 <!--*       Generated from PreTeXt source      *-->
-<!--*       on 2026-01-09T12:50:57-05:00       *-->
+<!--*       on 2026-01-09T13:00:08-05:00       *-->
 <!--*   A recent stable commit (2022-07-01):   *-->
 <!--* 6c761d3dba23af92cba35001c852aac04ae99a5f *-->
 <!--*                                          *-->

course/lunr-pretext-search-index.js

@@ -16,7 +16,7 @@ var ptx_lunr_docs = [
   "type": "Worksheet",
   "number": "",
   "title": "Calculus Review",
-  "body": " Calculus Review    In Calculus I, you learned about derivatives, antiderivatives, and definite integrals. All of these will make an appearance in the context of probability density functions, cumulative distribution functions, and probability calculations in continuous sample spaces, so it will be useful to refresh your memory and practice some calculations.      The Power Rule for derivatives states:     "
+  "body": " Calculus Review    In Calculus I, you learned about derivatives, antiderivatives, and definite integrals. All of these will make an appearance in the context of probability density functions, cumulative distribution functions, and probability calculations in continuous sample spaces, so it will be useful to refresh your memory and practice some calculations.      The Power Rule for derivatives states:       The Power Rule for antiderivatives states:       Practice with the following derivatives:       Practice with the following antiderivatives:       If is an antiderivative of i.e., if then the Fundamental Theorem of Calculus (FTC) says: If is a probability density function (don't worry about what that means for now), then integrals such as are used to calculate certain probabilities, and so are function values of the form .      Practice with the following integrals:     "
 },
 {
   "id": "recitation-calculus-review-3",
@@ -26,6 +26,51 @@ var ptx_lunr_docs = [
   "number": "1",
   "title": "",
   "body": "  The Power Rule for derivatives states:    "
+},
+{
+  "id": "recitation-calculus-review-4",
+  "level": "2",
+  "url": "recitation-calculus-review.html#recitation-calculus-review-4",
+  "type": "Worksheet Exercise",
+  "number": "2",
+  "title": "",
+  "body": "  The Power Rule for antiderivatives states:    "
+},
+{
+  "id": "recitation-calculus-review-5",
+  "level": "2",
+  "url": "recitation-calculus-review.html#recitation-calculus-review-5",
+  "type": "Worksheet Exercise",
+  "number": "3",
+  "title": "",
+  "body": "  Practice with the following derivatives:    "
+},
+{
+  "id": "recitation-calculus-review-6",
+  "level": "2",
+  "url": "recitation-calculus-review.html#recitation-calculus-review-6",
+  "type": "Worksheet Exercise",
+  "number": "4",
+  "title": "",
+  "body": "  Practice with the following antiderivatives:    "
+},
+{
+  "id": "thm-FTC",
+  "level": "2",
+  "url": "recitation-calculus-review.html#thm-FTC",
+  "type": "Theorem",
+  "number": "1",
+  "title": "",
+  "body": "  If is an antiderivative of i.e., if then the Fundamental Theorem of Calculus (FTC) says: If is a probability density function (don't worry about what that means for now), then integrals such as are used to calculate certain probabilities, and so are function values of the form .   "
+},
+{
+  "id": "recitation-calculus-review-8",
+  "level": "2",
+  "url": "recitation-calculus-review.html#recitation-calculus-review-8",
+  "type": "Worksheet Exercise",
+  "number": "5",
+  "title": "",
+  "body": "  Practice with the following integrals:    "
 }
 ]
 

course/recitation-calculus-review-printable.html

@@ -189,14 +189,70 @@ eBookConfig.enable_chatcodes =  false;
 <div class="para logical" id="recitation-calculus-review-3-1-1">
 <div class="para">The Power Rule for derivatives states:</div>
 <div class="displaymath process-math" id="recitation-calculus-review-3-1-1-1">
-\begin{gather}
+\begin{gather*}
-\frac{d}{dx}\left( x^n \right) = \tag{0}
+\frac{d}{dx}\left( x^n \right) = 
-\end{gather}
+\end{gather*}
 </div>
 <div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
-<div class="workspace" data-space="2in"></div>
+<div class="autopermalink" data-description="Worksheet Exercise 1"><a href="#recitation-calculus-review-3" title="Copy heading and permalink for Worksheet Exercise 1" aria-label="Copy heading and permalink for Worksheet Exercise 1">🔗</a></div></article><article class="exercise exercise-like" id="recitation-calculus-review-4"><h3 class="heading"><span class="codenumber">2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
-<div class="autopermalink" data-description="Worksheet Exercise 1"><a href="#recitation-calculus-review-3" title="Copy heading and permalink for Worksheet Exercise 1" aria-label="Copy heading and permalink for Worksheet Exercise 1">🔗</a></div></article><div class="autopermalink" data-description="Worksheet: Calculus Review"><a href="#recitation-calculus-review" title="Copy heading and permalink for Worksheet: Calculus Review" aria-label="Copy heading and permalink for Worksheet: Calculus Review">🔗</a></div></section>
+<div class="para logical" id="recitation-calculus-review-4-1-1">
+<div class="para">The Power Rule for antiderivatives states:</div>
+<div class="displaymath process-math" id="recitation-calculus-review-4-1-1-1">
+\begin{gather*}
+\int\left( x^n \right)\ dx = 
+\end{gather*}
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Worksheet Exercise 2"><a href="#recitation-calculus-review-4" title="Copy heading and permalink for Worksheet Exercise 2" aria-label="Copy heading and permalink for Worksheet Exercise 2">🔗</a></div></article><article class="exercise exercise-like" id="recitation-calculus-review-5"><h3 class="heading"><span class="codenumber">3<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
+<div class="para logical" id="recitation-calculus-review-5-1-1">
+<div class="para">Practice with the following derivatives:</div>
+<div class="displaymath process-math" id="recitation-calculus-review-5-1-1-1">
+\begin{align*}
+\frac{d}{dx}\left( 2x^2 + x^{-3} + 4\sqrt{x} \right) \amp = \\
+\frac{d}{dx}\left( \frac{1}{x} + 3e^{2x} + x^e + \pi^e \right) \amp = 
+\end{align*}
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-5-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Worksheet Exercise 3"><a href="#recitation-calculus-review-5" title="Copy heading and permalink for Worksheet Exercise 3" aria-label="Copy heading and permalink for Worksheet Exercise 3">🔗</a></div></article><article class="exercise exercise-like" id="recitation-calculus-review-6"><h3 class="heading"><span class="codenumber">4<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
+<div class="para logical" id="recitation-calculus-review-6-1-1">
+<div class="para">Practice with the following antiderivatives:</div>
+<div class="displaymath process-math" id="recitation-calculus-review-6-1-1-1">
+\begin{align*}
+\int  2x^2 + x^{-3} + 4\sqrt{x} \ dx \amp = \\
+\int  \frac{1}{x} + 3e^{2x} + x^e + \pi^e \ dx \amp = 
+\end{align*}
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-6-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Worksheet Exercise 4"><a href="#recitation-calculus-review-6" title="Copy heading and permalink for Worksheet Exercise 4" aria-label="Copy heading and permalink for Worksheet Exercise 4">🔗</a></div></article><article class="theorem theorem-like" id="thm-FTC"><h3 class="heading">
+<span class="type">Theorem</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">1</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
+</h3>
+<div class="para logical" id="thm-FTC-1-1">
+<div class="para">If <span class="process-math">\(F(x)\)</span> is an antiderivative of <span class="process-math">\(f(x)\)</span>—i.e., if <span class="process-math">\(F'(x) = f(x)\)</span>—then the Fundamental Theorem of Calculus (FTC) says:</div>
+<div class="displaymath process-math" id="thm-FTC-1-1-6">
+\begin{gather*}
+\int_a^b f(x)\ dx = F(x)\bigg|_a^b = F(b) - F(a).  
+\end{gather*}
+</div>
+<div class="para">If <span class="process-math">\(f(x)\)</span> is a probability density function (don’t worry about what that means for now), then integrals such as <span class="process-math">\(\int_a^b f(x)\ dx\)</span> are used to calculate certain probabilities, and so are function values of the form <span class="process-math">\(F(x)\text{.}\)</span>
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#thm-FTC-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Theorem 1"><a href="#thm-FTC" title="Copy heading and permalink for Theorem 1" aria-label="Copy heading and permalink for Theorem 1">🔗</a></div></article><article class="exercise exercise-like" id="recitation-calculus-review-8"><h3 class="heading"><span class="codenumber">5<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
+<div class="para logical" id="recitation-calculus-review-8-1-1">
+<div class="para">Practice with the following integrals:</div>
+<div class="displaymath process-math" id="recitation-calculus-review-8-1-1-1">
+\begin{align*}
+\int_0^1 \frac{3}{2} x^{3/2} \ dx \amp = \\
+\int_0^x 3e^{-3t} \ dt \amp = 
+\end{align*}
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-8-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Worksheet Exercise 5"><a href="#recitation-calculus-review-8" title="Copy heading and permalink for Worksheet Exercise 5" aria-label="Copy heading and permalink for Worksheet Exercise 5">🔗</a></div></article><div class="autopermalink" data-description="Worksheet: Calculus Review"><a href="#recitation-calculus-review" title="Copy heading and permalink for Worksheet: Calculus Review" aria-label="Copy heading and permalink for Worksheet: Calculus Review">🔗</a></div></section>
 </div>
 <div id="ptx-content-footer" class="ptx-content-footer">
 <a class="previous-button button" href="recitations.html" title="Previous"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cb;</span><span class="name">Prev</span></a><a class="top-button button" href="#" title="Top"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5ce;</span><span class="name">Top</span></a><span class="next-button button disabled"><span class="name">Next</span><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cc;</span></span>

course/recitation-calculus-review.html

@@ -174,14 +174,70 @@ eBookConfig.enable_chatcodes =  false;
 <div class="para logical" id="recitation-calculus-review-3-1-1">
 <div class="para">The Power Rule for derivatives states:</div>
 <div class="displaymath process-math" id="recitation-calculus-review-3-1-1-1">
-\begin{gather}
+\begin{gather*}
-\frac{d}{dx}\left( x^n \right) = \tag{0}
+\frac{d}{dx}\left( x^n \right) = 
-\end{gather}
+\end{gather*}
 </div>
 <div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
 </div>
-<div class="workspace" data-space="2in"></div>
+<div class="autopermalink" data-description="Worksheet Exercise 1"><a href="#recitation-calculus-review-3" title="Copy heading and permalink for Worksheet Exercise 1" aria-label="Copy heading and permalink for Worksheet Exercise 1">🔗</a></div></article><article class="exercise exercise-like" id="recitation-calculus-review-4"><h3 class="heading"><span class="codenumber">2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
-<div class="autopermalink" data-description="Worksheet Exercise 1"><a href="#recitation-calculus-review-3" title="Copy heading and permalink for Worksheet Exercise 1" aria-label="Copy heading and permalink for Worksheet Exercise 1">🔗</a></div></article><div class="autopermalink" data-description="Worksheet: Calculus Review"><a href="#recitation-calculus-review" title="Copy heading and permalink for Worksheet: Calculus Review" aria-label="Copy heading and permalink for Worksheet: Calculus Review">🔗</a></div></section></div>
+<div class="para logical" id="recitation-calculus-review-4-1-1">
+<div class="para">The Power Rule for antiderivatives states:</div>
+<div class="displaymath process-math" id="recitation-calculus-review-4-1-1-1">
+\begin{gather*}
+\int\left( x^n \right)\ dx = 
+\end{gather*}
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Worksheet Exercise 2"><a href="#recitation-calculus-review-4" title="Copy heading and permalink for Worksheet Exercise 2" aria-label="Copy heading and permalink for Worksheet Exercise 2">🔗</a></div></article><article class="exercise exercise-like" id="recitation-calculus-review-5"><h3 class="heading"><span class="codenumber">3<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
+<div class="para logical" id="recitation-calculus-review-5-1-1">
+<div class="para">Practice with the following derivatives:</div>
+<div class="displaymath process-math" id="recitation-calculus-review-5-1-1-1">
+\begin{align*}
+\frac{d}{dx}\left( 2x^2 + x^{-3} + 4\sqrt{x} \right) \amp = \\
+\frac{d}{dx}\left( \frac{1}{x} + 3e^{2x} + x^e + \pi^e \right) \amp = 
+\end{align*}
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-5-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Worksheet Exercise 3"><a href="#recitation-calculus-review-5" title="Copy heading and permalink for Worksheet Exercise 3" aria-label="Copy heading and permalink for Worksheet Exercise 3">🔗</a></div></article><article class="exercise exercise-like" id="recitation-calculus-review-6"><h3 class="heading"><span class="codenumber">4<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
+<div class="para logical" id="recitation-calculus-review-6-1-1">
+<div class="para">Practice with the following antiderivatives:</div>
+<div class="displaymath process-math" id="recitation-calculus-review-6-1-1-1">
+\begin{align*}
+\int  2x^2 + x^{-3} + 4\sqrt{x} \ dx \amp = \\
+\int  \frac{1}{x} + 3e^{2x} + x^e + \pi^e \ dx \amp = 
+\end{align*}
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-6-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Worksheet Exercise 4"><a href="#recitation-calculus-review-6" title="Copy heading and permalink for Worksheet Exercise 4" aria-label="Copy heading and permalink for Worksheet Exercise 4">🔗</a></div></article><article class="theorem theorem-like" id="thm-FTC"><h3 class="heading">
+<span class="type">Theorem</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">1</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
+</h3>
+<div class="para logical" id="thm-FTC-1-1">
+<div class="para">If <span class="process-math">\(F(x)\)</span> is an antiderivative of <span class="process-math">\(f(x)\)</span>—i.e., if <span class="process-math">\(F'(x) = f(x)\)</span>—then the Fundamental Theorem of Calculus (FTC) says:</div>
+<div class="displaymath process-math" id="thm-FTC-1-1-6">
+\begin{gather*}
+\int_a^b f(x)\ dx = F(x)\bigg|_a^b = F(b) - F(a).  
+\end{gather*}
+</div>
+<div class="para">If <span class="process-math">\(f(x)\)</span> is a probability density function (don’t worry about what that means for now), then integrals such as <span class="process-math">\(\int_a^b f(x)\ dx\)</span> are used to calculate certain probabilities, and so are function values of the form <span class="process-math">\(F(x)\text{.}\)</span>
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#thm-FTC-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Theorem 1"><a href="#thm-FTC" title="Copy heading and permalink for Theorem 1" aria-label="Copy heading and permalink for Theorem 1">🔗</a></div></article><article class="exercise exercise-like" id="recitation-calculus-review-8"><h3 class="heading"><span class="codenumber">5<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
+<div class="para logical" id="recitation-calculus-review-8-1-1">
+<div class="para">Practice with the following integrals:</div>
+<div class="displaymath process-math" id="recitation-calculus-review-8-1-1-1">
+\begin{align*}
+\int_0^1 \frac{3}{2} x^{3/2} \ dx \amp = \\
+\int_0^x 3e^{-3t} \ dt \amp = 
+\end{align*}
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-8-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Worksheet Exercise 5"><a href="#recitation-calculus-review-8" title="Copy heading and permalink for Worksheet Exercise 5" aria-label="Copy heading and permalink for Worksheet Exercise 5">🔗</a></div></article><div class="autopermalink" data-description="Worksheet: Calculus Review"><a href="#recitation-calculus-review" title="Copy heading and permalink for Worksheet: Calculus Review" aria-label="Copy heading and permalink for Worksheet: Calculus Review">🔗</a></div></section></div>
 <div id="ptx-content-footer" class="ptx-content-footer">
 <a class="previous-button button" href="recitations.html" title="Previous"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cb;</span><span class="name">Prev</span></a><a class="top-button button" href="#" title="Top"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5ce;</span><span class="name">Top</span></a><span class="next-button button disabled"><span class="name">Next</span><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cc;</span></span>
 </div></main>