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2026-01-15 20:01:00 -05:00
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@@ -165,13 +165,23 @@ eBookConfig.enable_chatcodes = false;
<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>
<ul class="structural toc-item-list"><li class="toc-item toc-subsection">
<ul class="structural toc-item-list">
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<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>
<ul class="structural toc-item-list">
<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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<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>
<ul class="structural toc-item-list">
<li class="toc-item toc-subsubsection"><div class="toc-title-box"><a href="notes-week-01.html#subsubsec-Conditional-Probability" class="internal"><span class="title">Conditional Probability</span></a></div></li>
<li class="toc-item toc-subsubsection"><div class="toc-title-box"><a href="notes-week-01.html#subsubsec-Diagnostic-Testing" class="internal"><span class="title">Diagnostic Testing</span></a></div></li>
<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>
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@@ -230,7 +240,7 @@ 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">22</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">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>
</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>
@@ -241,7 +251,7 @@ 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>
</div>
<div class="autopermalink" data-description="Theorem 22: Fundamental Theorem of Calculus"><a href="#thm-FTC" title="Copy heading and permalink for Theorem 22: Fundamental Theorem of Calculus" aria-label="Copy heading and permalink for Theorem 22: 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 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>
<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>