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2026-01-22 10:16:02 -05:00
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</li>
<li class="toc-item toc-chapter">
<div class="toc-title-box"><a href="ch-notes.html" class="internal"><span class="title">Class Notes</span></a></div>
<ul class="structural toc-item-list"><li class="toc-item toc-section">
<div class="toc-title-box"><a href="notes-week-01.html" class="internal"><span class="title">Week 1</span></a></div>
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<li class="toc-item toc-subsection">
<div class="toc-title-box"><a href="notes-week-01.html#notes-week-01-3" class="internal"><span class="title">Tuesday 1/13</span></a></div>
<li class="toc-item toc-section">
<div class="toc-title-box"><a href="notes-01-13.html" class="internal"><span class="title">Tuesday, Jan 13</span></a></div>
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<li class="toc-item toc-subsubsection"><div class="toc-title-box"><a href="notes-week-01.html#subsubsec-Sets" class="internal"><span class="title">Sec 1.1: Sets</span></a></div></li>
<li class="toc-item toc-subsubsection"><div class="toc-title-box"><a href="notes-week-01.html#subsubsec-Probability" class="internal"><span class="title">Sec 1.2: Probability</span></a></div></li>
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<li class="toc-item toc-subsection">
<div class="toc-title-box"><a href="notes-week-01.html#notes-week-01-4" class="internal"><span class="title">Thursday 1/15</span></a></div>
<li class="toc-item toc-section">
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<li class="toc-item toc-subsubsection"><div class="toc-title-box"><a href="notes-week-01.html#subsubsec-Independent-Events" class="internal"><span class="title">Independent Events</span></a></div></li>
<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-15.html#subsec-Conditional-Probability" class="internal"><span class="title">Sec 1.3: Conditional Probability</span></a></div></li>
<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-15.html#subsec-Diagnostic-Testing" class="internal"><span class="title">Diagnostic Testing</span></a></div></li>
<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-15.html#subsec-Independent-Events" class="internal"><span class="title">Sec 1.4: Independent Events</span></a></div></li>
</ul>
</li>
<li class="toc-item toc-section">
<div class="toc-title-box"><a href="notes-01-20.html" class="internal"><span class="title">Tuesday, Jan 20</span></a></div>
<ul class="structural toc-item-list"><li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-20.html#subsec-Discrete-Random-Variables" class="internal"><span class="title">Sec 2.1: Random Variables</span></a></div></li></ul>
</li>
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<li class="toc-item toc-chapter contains-active">
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@@ -204,9 +220,9 @@ eBookConfig.enable_chatcodes = false;
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<section class="worksheet" id="recitation-calculus-review" data-margins="0.75in 0.75in 0.75in 0.75in"><h2 class="heading hide-type">
<section class="worksheet" id="recitation-calculus-review" data-margins="0.75in 0.75in 0.75in 0.75in"><h1 class="heading hide-type">
<span class="type">Worksheet</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber"></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Calculus Review</span><div class="print-links"><a href="recitation-calculus-review-printable.html" class="print-link" title="Print preview"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe8ad;</span></a></div>
</h2>
</h1>
<section class="introduction" id="recitation-calculus-review-2"><div class="para" id="recitation-calculus-review-2-1">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.<div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div></section><section class="onepage" id="recitation-calculus-review-3"><article class="exercise exercise-like" id="recitation-calculus-review-3-1"><h3 class="heading"><span class="codenumber">1<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
<div class="para logical" id="recitation-calculus-review-3-1-1-1">
@@ -255,7 +271,7 @@ eBookConfig.enable_chatcodes = false;
</div>
<div class="workspace" data-space="2cm"></div>
<div class="autopermalink" data-description="Task 4.b"><a href="#recitation-calculus-review-3-4-3" title="Copy heading and permalink for Task 4.b" aria-label="Copy heading and permalink for Task 4.b">🔗</a></div></article><div class="autopermalink" data-description="Worksheet Exercise 4"><a href="#recitation-calculus-review-3-4" title="Copy heading and permalink for Worksheet Exercise 4" aria-label="Copy heading and permalink for Worksheet Exercise 4">🔗</a></div></article></section><section class="onepage" id="recitation-calculus-review-4"><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">34</span><span class="period heading-divison-mark heading-divison-mark__period">.</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Fundamental Theorem of Calculus.</span>
<span class="type">Theorem</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">40</span><span class="period heading-divison-mark heading-divison-mark__period">.</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Fundamental Theorem of Calculus.</span>
</h3>
<div class="para logical" id="thm-FTC-2-1">
<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:</div>
@@ -266,7 +282,7 @@ eBookConfig.enable_chatcodes = false;
</div>
<div class="autopermalink" data-description="Paragraph"><a href="#thm-FTC-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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<div class="autopermalink" data-description="Theorem 34: Fundamental Theorem of Calculus"><a href="#thm-FTC" title="Copy heading and permalink for Theorem 34: Fundamental Theorem of Calculus" aria-label="Copy heading and permalink for Theorem 34: Fundamental Theorem of Calculus">🔗</a></div></article><div class="para" id="recitation-calculus-review-4-2">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, as are values of the form <span class="process-math">\(F(x)\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-4-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
<div class="autopermalink" data-description="Theorem 40: Fundamental Theorem of Calculus"><a href="#thm-FTC" title="Copy heading and permalink for Theorem 40: Fundamental Theorem of Calculus" aria-label="Copy heading and permalink for Theorem 40: Fundamental Theorem of Calculus">🔗</a></div></article><div class="para" id="recitation-calculus-review-4-2">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, as are values of the form <span class="process-math">\(F(x)\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-4-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div>
<article class="exercise exercise-like" id="recitation-calculus-review-4-3"><h3 class="heading"><span class="codenumber">5<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
<div class="introduction" id="recitation-calculus-review-4-3-1"><div class="para" id="recitation-calculus-review-4-3-1-1">Practice with the following integrals:<div class="autopermalink" data-description="Paragraph"><a href="#recitation-calculus-review-4-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>