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You can mix-and-match problems from other user-contributed courses, add problems from the user-contributed problem repository, or write your own problems.\u003c/p\u003e\u003cp dir=\"ltr\"\u003e\u003cstrong\u003eHow to use this course\u003c/strong\u003e\u003c/p\u003e\u003col\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eHomework\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Assign high quality problems with hints and personalized feedback to develop problem-solving skills.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eTesting\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Create summative secure online quizzes and tests in minutes.\u0026nbsp;\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eSupplementary resources:\u003c/strong\u003e Embed videos, class notes, and applets alongside assignments.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eIntervention:\u003c/strong\u003e Use rich analytics to identify and monitor at-risk students for timely intervention.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eAnalytics:\u003c/strong\u003e Drill down into student performance and identify problematic or difficult topics.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eFlipped classroom:\u003c/strong\u003e Assign pre-class assignments. Save precious class time for discussions.\u003c/li\u003e\u003cli dir=\"ltr\"\u003e\u003cstrong\u003eEmporium classes:\u003c/strong\u003e Use Edfinity for individual/group work for large enrollment sections in labs.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003eEdfinity is a full-featured homework system that supports mathematically-aware problems with algebraic input, evaluation of mathematical expressions, randomized variants, prerequisite pathways for personalized learning, collaboration, coordinated courses, flexible configuration of students\u0026rsquo; experience, and complete customization of assignments.\u003c/p\u003e","description_more":"","price":40.0,"sort_order":0,"active":true,"individual_license":false,"section_id":"5c6c57d0d635b100047a271a","permissive_license":false,"type":"course","year":null,"section_license":true,"taxable":false,"purchasable":true,"related_product_ids":["5c533d7d78811e0e5904234d","5c58eabf4a8e21002b802892","5c6c7c0e7758b300165b7b6e","5c6cb0717758b325775b77fe","5f16ff9e4a1e8d1366b8f2b1"],"paired_product_id":null,"min_quantity":null,"max_quantity":null,"audience":"educator_audience","site_ids":["55843bd46435650003000000"],"package_price":null,"show_toc":true,"author_roles":[],"author_role_title":"Contributors (Alphabetical)","institution":null,"tags_array":["calculus","oer"],"hidden_tags":["oer","adaptive"],"meta_description":null,"term_pricing":true,"curricula":null,"curricula_course":null,"highlights":"\u003cdiv class=\"mb-3\"\u003e\u003cspan class=\"fa fa-subscript fa-fw mr-2\"\u003e\u003c/span\u003e \u003cstrong\u003eInteractive, algorithmic problems\u003cbr\u003e\u003c/strong\u003eAlgebraic, graphing, open response; randomized variants, hints, and tips\u003c/div\u003e\u003cdiv class=\"mb-3\"\u003e\u003cspan class=\"fa fa-hand-holding-heart fa-fw mr-2\"\u003e\u003c/span\u003e\u003cstrong\u003eAdaptive learning and personalization\u003cbr\u003e\u003c/strong\u003eEach student receives personalized support\u003cbr\u003eto fill learning gaps.\u003c/div\u003e\u003cdiv class=\"mb-3\"\u003e\u003cspan class=\"fa fa-fw fa-code-branch mr-2\"\u003e\u003c/span\u003e\u003cstrong\u003eCorequisite course structures\u003cbr\u003e\u003c/strong\u003eUse pre-built corequisite content,\u003cbr\u003eor create your own.\u003c/div\u003e\u003cdiv class=\"mb-3\"\u003e\u003cspan class=\"fa fa-hands-helping fa-fw mr-2\"\u003e\u003c/span\u003e\u003cstrong\u003eLMS integration and accessibility\u003cbr\u003e\u003c/strong\u003eConnect to your LMS in minutes. \u003ca class=\"”underline”\" href=\"http://edfinity.com/vpat\" target=\"_blank\"\u003eVPAT here\u003c/a\u003e.\u003c/div\u003e\u003cdiv class=\"mb-3\"\u003e\u003cspan class=\"fa fa-plug fa-fw mr-2\"\u003e\u003c/span\u003e\u003cstrong\u003eWeBWorK-compatible\u003cbr\u003e\u003c/strong\u003eImport and author WeBWorK problems.\u003c/div\u003e","preview_assignment":{"id":"5c6c57d0d635b100047a271d","name":"1.1 An Introduction to Limits","product":{"id":"5c735527c6e851001a2555ad","name":"APEX Calculus 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class=\"PGML\"\u003e\nA function \\(f\\) and value \\(a\\) are given below.\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\\[f(x) = \\frac{1}{x + 5}, \\qquad a = 6\\]\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\nApproximate the limit of the difference quotient,\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\\[\\lim\\limits_{h \\to 0} \\frac{f(a+h) - f(a)}{h},\\]\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\nusing \\(h = \\pm 0.1, \\pm 0.01\\).\n\u003cb\u003e(Round your answer to within three decimal places if necessary, but \ndo not round until your final computation.)\u003c/b\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003col type=\"a\" style=\"margin:0; padding-left:2.25em\"\u003e\n\u003cli\u003eWhen \\(h = 0.1\\), \\(\\dfrac{f(a+h) - f(a)}{h} =\\) \u003cinput type=\"text\" class=\"codeshard\" size=\"2\" name=\"AnSwEr0001\" id=\"AnSwEr0001\" aria-label=\"answer 1 \" dir=\"auto\" autocomplete=\"off\" autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0001\" value=\"\"\u003e\n.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eWhen \\(h = -0.1\\), \\(\\dfrac{f(a+h) - f(a)}{h} =\\) \u003cinput type=\"text\" class=\"codeshard\" size=\"2\" name=\"AnSwEr0002\" id=\"AnSwEr0002\" aria-label=\"answer 2 \" dir=\"auto\" autocomplete=\"off\" autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0002\" value=\"\"\u003e\n.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eWhen \\(h = 0.01\\), \\(\\dfrac{f(a+h) - f(a)}{h} =\\) \u003cinput type=\"text\" class=\"codeshard\" size=\"2\" name=\"AnSwEr0003\" id=\"AnSwEr0003\" aria-label=\"answer 3 \" dir=\"auto\" autocomplete=\"off\" autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0003\" value=\"\"\u003e\n.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eWhen \\(h = -0.01\\), \\(\\dfrac{f(a+h) - f(a)}{h} =\\) \u003cinput type=\"text\" class=\"codeshard\" size=\"2\" name=\"AnSwEr0004\" id=\"AnSwEr0004\" aria-label=\"answer 4 \" dir=\"auto\" autocomplete=\"off\" autocorrect=\"off\" autocapitalize=\"off\" spellcheck=\"false\" value=\"\"\u003e\n\u003cinput type=\"hidden\" name=\"previous_AnSwEr0004\" value=\"\"\u003e\n.\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class=\"solution\"\u003e\n\u003cp\u003e\u003cb\u003eSolution:\u003c/b\u003e \u003cbr\u003e\nSubstitute each value of \\(h\\) into the expression\n\\(\\dfrac{f(a+h) - f(a)}{h}\\).\n\u003cbr\u003e\n\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n\u003ctable border=\"1\" style=\"text-align:center;\"\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(h\\) \u003c/td\u003e\n\u003ctd\u003e \\(\\frac{f(a+h) - f(a)}{h}\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(0.1\\) \u003c/td\u003e\n\u003ctd\u003e \\(-0.00819000819000819\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(-0.1\\) \u003c/td\u003e\n\u003ctd\u003e \\(-0.00834028356964137\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(0.01\\) \u003c/td\u003e\n\u003ctd\u003e \\(-0.00825695648583932\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(-0.01\\) \u003c/td\u003e\n\u003ctd\u003e \\(-0.00827198279427579\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003c/table\u003e\n\u003cbr\u003e\n\u003c/div\u003e\n\n\u003c/div\u003e","static_html":"\u003cdiv class=\"PGML\"\u003e\nA function \\(f\\) and value \\(a\\) are given below.\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\\[f(x) = \\frac{1}{x + 5}, \\qquad a = 6\\]\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\nApproximate the limit of the difference quotient,\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\\[\\lim\\limits_{h \\to 0} \\frac{f(a+h) - f(a)}{h},\\]\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\nusing \\(h = \\pm 0.1, \\pm 0.01\\).\n\u003cb\u003e(Round your answer to within three decimal places if necessary, but \ndo not round until your final computation.)\u003c/b\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003col type=\"a\" style=\"margin:0; padding-left:2.25em\"\u003e\n\u003cli\u003eWhen \\(h = 0.1\\), \\(\\dfrac{f(a+h) - f(a)}{h} =\\) \u003cspan class=\"ww-blank\" name=\"AnSwEr0001\"\u003e \u003c/span\u003e\n\n.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eWhen \\(h = -0.1\\), \\(\\dfrac{f(a+h) - f(a)}{h} =\\) \u003cspan class=\"ww-blank\" name=\"AnSwEr0002\"\u003e \u003c/span\u003e\n\n.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eWhen \\(h = 0.01\\), \\(\\dfrac{f(a+h) - f(a)}{h} =\\) \u003cspan class=\"ww-blank\" name=\"AnSwEr0003\"\u003e \u003c/span\u003e\n\n.\u003c/li\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003cli\u003eWhen \\(h = -0.01\\), \\(\\dfrac{f(a+h) - f(a)}{h} =\\) \u003cspan class=\"ww-blank\" name=\"AnSwEr0004\"\u003e \u003c/span\u003e\n\n.\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv style=\"margin-top:1em\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class=\"solution\"\u003e\n\u003cp\u003e\u003cb\u003eSolution:\u003c/b\u003e \u003cbr\u003e\nSubstitute each value of \\(h\\) into the expression\n\\(\\dfrac{f(a+h) - f(a)}{h}\\).\n\u003cbr\u003e\n\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n\u003ctable border=\"1\" style=\"text-align:center;\"\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(h\\) \u003c/td\u003e\n\u003ctd\u003e \\(\\frac{f(a+h) - f(a)}{h}\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(0.1\\) \u003c/td\u003e\n\u003ctd\u003e \\(-0.00819000819000819\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(-0.1\\) \u003c/td\u003e\n\u003ctd\u003e \\(-0.00834028356964137\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(0.01\\) \u003c/td\u003e\n\u003ctd\u003e \\(-0.00825695648583932\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003ctr\u003e\n\u003ctd\u003e \\(-0.01\\) \u003c/td\u003e\n\u003ctd\u003e \\(-0.00827198279427579\\) \u003c/td\u003e\n\u003c/tr\u003e\n\n        \u003c/table\u003e\n\u003cbr\u003e\n\u003c/div\u003e\n\n\u003c/div\u003e","timeout":false,"header_text":{"css":[],"js":[],"inlinejs":[]}}],"readonly":{"created_at":"2023-07-13T19:43:26.888Z","updated_at":"2023-07-13T19:43:26.888Z","version":110,"user_id":"58ecdcd48ccf1800120c8ac3","name":"Algorithmic (WebWorK)","skill_ids":["5a139c2bc0421000041a00a2","5a141cc2ac370c0004c7588d","5a139c2bc0421000041a00a2","5a141cc2ac370c0004c7588d","5a1f39a1dbc33f00041a1914","5a141cc2ac370c0004c7588d","5a1f39a1dbc33f00041a1914"],"current_digest":"rIgfyhCfgO2jq1anz0TSGPpixzVHVkrl/byssvi7EPs=","tags":"","points":4.0,"type":"webwork","multipart":true,"shallow":true,"static":true,"sources":[],"owned":false,"url":"/problems/64b053ded9aed500023f13a7","searchable_text":"Substitute each value of h into the expression dfrac f a h f a h BCENTER begintable 2 row h frac f a h f a h firstrow row h1 ans1 secondrow row hx1 ans2 thirdrow row h01 ans3 fourthrow row hx01 ans4 fifthrow endtable ECENTER A function f and value a are given below f x frac b x c qquad a a Approximate the limit of the difference quotient limlimits h to 0 frac f a h f a h using h pm 0 1 pm 0 01 Round your answer to within three decimal places if necessary but do not round until your final computation a When h h1 dfrac f a h f a h b When h hx1 dfrac f a h f a h c When h h01 dfrac f a h f a h d When h hx01 dfrac f a h f a h","abilities":["read"]}},"readonly":{"shallow":true}}},"readonly":{"level_range":"13","created_at":"2019-02-25T02:38:31.563Z","updated_at":"2026-03-15T19:38:19.296Z","tags":"calculus,oer","author_ids":[],"licensed":true,"thumbnail":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c735527c6e851001a2555ad/thumb_apex-calculus.png","free":false,"user_price":40.0,"term_price":40.0,"displayed_price":40.0,"levels":"13","author_role_title":"Contributors (Alphabetical)","abilities":[],"section":{"id":"5c6c57d0d635b100047a271a","name":"APEX Calculus (Hartman) v2"}},"image":{"identifier":"apex-calculus.png","size":20505,"url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c735527c6e851001a2555ad/apex-calculus.png","thumb_url":"https://d1q29jrdo98n6g.cloudfront.net/uploads/product/image/5c735527c6e851001a2555ad/thumb_apex-calculus.png"},"related_products":[{"id":"5c533d7d78811e0e5904234d","name":"OpenStax Calculus Volume 1","price":40.0,"individual_license":false,"user_price":40.0},{"id":"5c58eabf4a8e21002b802892","name":"Active Calculus (Boelkins)","price":40.0,"individual_license":false,"user_price":40.0},{"id":"5c6c7c0e7758b300165b7b6e","name":"OpenStax Calculus Volume 2","price":40.0,"individual_license":false,"user_price":40.0},{"id":"5c6cb0717758b325775b77fe","name":"OpenStax Calculus Volume 3","price":40.0,"individual_license":false,"user_price":40.0},{"id":"5f16ff9e4a1e8d1366b8f2b1","name":"Active Calculus Multivariable (Boelkins)","price":40.0,"individual_license":false,"user_price":40.0}],"toc":{"assignments":[{"id":"63068b2c39f3c800049c0975","name":"0 Edfinity Demo"},{"id":"5c6c57d0d635b100047a271d","name":"1.1 An Introduction to Limits"},{"id":"5c6c57d1d635b100047a276f","name":"1.2 Epsilon-Delta Definition of a Limit"},{"id":"5c6c57d1d635b100047a2793","name":"1.3 Finding Limits Analytically"},{"id":"5c6c57d2d635b100047a2802","name":"1.4 One Sided Limits"},{"id":"5c6c57d3d635b100047a286d","name":"1.5 Continuity"},{"id":"5c6c57d4d635b100047a28e6","name":"1.6 Limits Involving Infinity"},{"id":"5c6c57d5d635b100047a295d","name":"2.1 Instantaneous Rates of Change"},{"id":"5c6c57d6d635b100047a2990","name":"2.2 Interpretations of the Derivative"},{"id":"5c6c57d6d635b100047a29d1","name":"2.3 Basic Differentiation Rules"},{"id":"5c6c57d7d635b100047a2a39","name":"2.4 The Product and Quotient Rules"},{"id":"5c6c57d9d635b100047a2af8","name":"2.5 The Chain Rule"},{"id":"5c6c57dad635b100047a2b36","name":"2.6 Implicit Differentiation"},{"id":"5c6c57dbd635b100047a2b61","name":"2.7 Derivatives of Inverse Functions"},{"id":"5c6c57dcd635b100047a2bbd","name":"3.1 Extreme Values"},{"id":"5c6c57ded635b100047a2c5f","name":"3.2 The Mean Value Theorem"},{"id":"5c6c57dfd635b100047a2cc2","name":"3.3 Increasing and Decreasing Functions"},{"id":"5c6c57e0d635b100047a2d56","name":"3.4 Concavity and the Second Derivative"},{"id":"5c6c57e1d635b100047a2e27","name":"3.5 Curve Sketching"},{"id":"5c6c57e2d635b100047a2e66","name":"4.1 Newton's Method"},{"id":"5c6c57e3d635b100047a2ec9","name":"4.2 Related Rates"},{"id":"5c6c57e3d635b100047a2f12","name":"4.3 Optimization"},{"id":"5c6c57e4d635b100047a2f58","name":"4.4 Differentials"},{"id":"5c6c57e5d635b100047a2fb9","name":"5.1 Antiderivatives and Indefinite Integration"},{"id":"5c6c57e6d635b100047a3026","name":"5.2 The Definite Integral"},{"id":"5c6c57e7d635b100047a3097","name":"5.3 Riemann Sums"},{"id":"5c6c57e8d635b100047a3174","name":"5.4 The Fundamental Theorem 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Area"},{"id":"5c6c57f4d635b100047a3610","name":"7.5 Work"},{"id":"5c6c57f4d635b100047a3643","name":"7.6 Fluid Forces"},{"id":"5c6e5ac2bef7a6631d634c92","name":"8.1 Sequences"},{"id":"5c6e5aacbef7a663fe634cfc","name":"8.2 Infinite Series"},{"id":"5c6c57f7d635b100047a373d","name":"8.3 Integral and Comparison Tests"},{"id":"5c6e59f7bef7a663fe634c73","name":"8.4 The Ratio and Root Tests"},{"id":"5c6c57f9d635b100047a3848","name":"8.5 Alternating Series and Absolute Convergence"},{"id":"5c6e5cd4b1076c648156e8a9","name":"8.6 Power Series"},{"id":"5c6c57fad635b100047a38ff","name":"8.7 Taylor Polynomials"},{"id":"5c6c57fbd635b100047a3955","name":"8.8 Taylor Series"},{"id":"5c6e57ebb1076c648156e734","name":"9.1 Conic Sections"},{"id":"5c6e57d0bef7a6443b63548a","name":"9.2 Parametric Equations"},{"id":"5c6e57aeb1076c633456e746","name":"9.3 Calculus and Parametric Equations"},{"id":"5c6e578ebef7a6443b63547c","name":"9.4 Introduction to Polar Coordinates"},{"id":"5c6e5772b1076c641356e752","name":"9.5 Calculus and Polar Functions"},{"id":"5c6e562dbef7a6443b635426","name":"10.1 An Introduction to Cartesian Coordinates in Space"},{"id":"5c6e5656bef7a61c5563617f","name":"10.2 An Introduction to Vectors"},{"id":"5c6e56b2bef7a61c556361a4","name":"10.3 The Dot Product"},{"id":"5c6e56d5bef7a6443b635447","name":"10.4 The Cross Product"},{"id":"5c6e572cb1076c639956e738","name":"10.5 Lines"},{"id":"5c6e5752b1076c639956e74d","name":"10.6 Planes"},{"id":"5c6e55b0bef7a6451063559a","name":"11.1 Vector-Valued Functions"},{"id":"5c6e5595b1076c1cf256fe04","name":"11.2 Calculus and Vector-Valued Functions"},{"id":"5c6e5560b1076c447556efe5","name":"11.3 The Calculus of Motion"},{"id":"5c6e5539bef7a61c55636143","name":"11.4 Unit Tangent and Normal Vectors"},{"id":"5c6e550abef7a6443b6353fa","name":"11.5 The Arc Length Parameter and Curvature"},{"id":"5c6e54c9bef7a644a6635341","name":"12.1 Introduction to Multivariable Functions"},{"id":"5c6e5481bef7a6451063557a","name":"12.2 Limits and Continuity of Multivariable Functions"},{"id":"5c6e544abef7a644a663532c","name":"12.3 Partial Derivatives"},{"id":"5c6f80d1fc9ddb3cc34cac41","name":"12.4 Differentiability and the Total Differential"},{"id":"5c6c580ad635b100047a3f8b","name":"12.5 The Multivariable Chain Rule"},{"id":"5c6c580bd635b100047a3fc7","name":"12.6 Directional Derivatives"},{"id":"5c6e8218b1076c648156eb6a","name":"12.7 Tangent Lines, Normal Lines, and Tangent Planes"},{"id":"5c6c580cd635b100047a3ff9","name":"12.8 Extreme Values"},{"id":"5c6e620cbef7a66391634d29","name":"13.1 Iterated Integrals and Area"},{"id":"5c6e6228bef7a6631d634cf3","name":"13.2 Double Integration and Volume"},{"id":"5c6e6240bef7a662a7634d59","name":"13.3 Double Integration with Polar Coordinates"},{"id":"5c6f80ea7bc2b272858bb4de","name":"13.4 Center of Mass"},{"id":"5c6f80f47bc2b272048bb543","name":"13.5 Surface Area"},{"id":"5c6e6268b1076c648156e8dc","name":"13.6 Volume Between Surfaces and Triple Integration"},{"id":"5c6e627db1076c648156e8e5","name":"13.7 Triple Integration with Cylindrical and Spherical Coordinates"},{"id":"5c6e616fb1076c639956e8fa","name":"14.1 Line Integrals"},{"id":"5c6e617eb1076c648156e8c6","name":"14.2 Vector Fields"},{"id":"5c6e6194bef7a6631d634ced","name":"14.3 Line Integrals over Vector Fields"},{"id":"5c6e61abbef7a6631d634cf1","name":"14.4 Flow, Flux, Green's Theorem"},{"id":"5c6e8143bef7a663fe634ed4","name":"14.5 Parametrized Surfaces and Surface Area"},{"id":"5c6e61bbbef7a662a7634d45","name":"14.6 Surface Integrals"},{"id":"5c6e61cdbef7a662a7634d4e","name":"14.7(a) Stokes' Theorem"},{"id":"5c6e61dbbef7a662a7634d50","name":"14.7(b) The Divergence Theorem"}]}}