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@@ -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}
\frac{d}{dx}\left( x^n \right) = \tag{0}
\end{gather}
\begin{gather*}
\frac{d}{dx}\left( x^n \right) =
\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><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="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="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>
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