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2026-01-22 10:16:02 -05:00
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@@ -101,15 +101,15 @@ eBookConfig.allow_pairs = false;
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@@ -140,6 +140,17 @@ eBookConfig.enable_chatcodes = false;
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@@ -163,26 +174,31 @@ eBookConfig.enable_chatcodes = false;
</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>
<ul class="structural toc-item-list">
<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>
<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>
<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-13.html#subsec-Sets" class="internal"><span class="title">Sec 1.1: Sets</span></a></div></li>
<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-13.html#subsec-Probability" class="internal"><span class="title">Sec 1.2: Probability</span></a></div></li>
</ul>
</li>
<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">
<div class="toc-title-box"><a href="notes-01-15.html" class="internal"><span class="title">Thursday, Jan 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>
<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>
</ul>
</li></ul>
</li>
<li class="toc-item toc-chapter">
<div class="toc-title-box"><a href="quizzes.html" class="internal"><span class="title">Quizzes</span></a></div>
<ul class="structural toc-item-list"><li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-01.html" class="internal"><span class="title">Quiz 1</span></a></div></li></ul>
</li>
<li class="toc-item toc-chapter contains-active">
<div class="toc-title-box"><a href="recitations.html" class="internal"><span class="title">Recitations</span></a></div>
@@ -240,7 +256,7 @@ 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>
@@ -251,7 +267,7 @@ 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 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>