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AP Calculus AB
flashcards
Decks in class (190)
# Cards
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1.1.1 An Introduction to Thinkwell Calculus1
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1.1.2 The Two Questions of Calculus3
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1.1.3 Average Rates of Change14
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1.1.4 How to Do Math1
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1.2.1 Functions16
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1.2.2 Graphing Lines14
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1.2.3 Parabolas15
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1.2.4 Some Non-Euclidean Geometry1
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Chapter 1 Practice Test20
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Chapter 1 Test20
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2.1.1 Finding Rate of Change over an Interval18
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2.1.2 Finding Limits Graphically9
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2.1.3 The Formal Definition of a Limit6
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2.1.4 The Limit Laws, Part I7
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2.1.5 The Limit Laws, Part II17
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2.1.6 One-Sided Limits11
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2.1.7 The Squeeze Theorem13
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2.1.8 Continuity and Discontinuity13
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2.2.1 Evaluating Limits17
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2.2.2 Limits and Indeterminate Forms12
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2.2.3 Two Techniques for Evaluating Limits7
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2.2.4 An Overview of Limits11
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Chapter 2 Practice Test20
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Chapter 2 Test20
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3.1.1 Rates of Change, Secants, and Tangents12
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3.1.2 Finding Instantaneous Velocity14
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3.1.3 The Derivative13
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3.1.4 Differentiability9
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3.2.1 The Slope of a Tangent Line9
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3.2.2 Instantaneous Rate14
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3.2.3 The Equation of a Tangent Line17
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3.2.4 More on Instantaneous Rate8
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3.3.1 The Derivative of the Reciprocal Function19
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3.3.2 The Derivative of the Square Root Function16
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Chapter 3 Practice Test20
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Chapter 3 Test20
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4.1.1 A Shortcut for Finding Derivatives14
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4.1.2 A Quick Proof of the Power Rule12
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4.1.3 Uses of the Power Rule24
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4.2.1 The Product Rule12
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4.2.2 The Quotient Rule9
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4.3.1 An Introduction to the Chain Rule15
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4.3.2 Using the Chain Rule14
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4.3.3 Combining Computational Techniques14
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Chapter 4 Practice Test20
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Chapter 4 Test20
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5.1.1 A Review of Trigonometry13
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5.1.2 Graphing Trigonometric Functions10
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5.1.3 The Derivatives of Trigonometric Functions17
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5.1.4 The Number Pi16
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5.2.1 Graphing Exponential Functions13
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5.2.2 Derivatives of Exponential Functions8
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5.3.1 Evaluating Logarithmic Functions11
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5.3.2 The Derivative of the Natural Log Function10
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5.3.3 Using the Derivative Rules with Transcendental Functions8
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Chapter 5 Practice Test20
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Chapter 5 Test20
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6.1.1 An Introduction to Implicit Differentiation13
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6.1.2 Finding the Derivative Implicitly14
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6.2.1 Using Implicit Differentiation14
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6.2.2 Applying Implicit Differentiation9
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6.3.1 The Exponential and Natural Log Functions12
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6.3.2 Differentiating Logarithmic Functions12
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6.3.3 Logarithmic Differentiation14
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6.3.4 The Basics of Inverse Functions12
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6.3.5 Finding the Inverse of a Function12
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6.4.1 Derivatives of Inverse Function12
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6.5.1 The Inverse Sine, Cosine, and Tangent Functions12
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6.5.2 The Inverse Secant, Cosecant, and Cotangent Functions12
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6.5.3 Evaluating Inverse Trigonometric Functions12
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6.6.1 Derivatives of Inverse Trigonometric Functions12
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6.7.1 Defining the Hyperbolic Functions12
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6.7.2 Hyperbolic Identities12
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6.7.3 Derivatives of Hyperbolic Functions12
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Chapter 6 Practice Test20
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Chapter 6 Test20
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Practice Midterm Exam20
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Midterm Exam20
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7.1.1 Acceleration and the Derivative9
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7.1.2 Solving Word Problems Involving Distance and Velocity15
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7.2.1 Higher-Order Derivatives and Linear Approximation14
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7.2.2 Using the Tangent Line Approximation Formula14
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7.2.3 Newton's Method6
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7.3.1 The Connection Between Slope and Optimization12
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7.3.2 The Fence Problem8
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7.3.3 The Box Problem8
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7.3.4 The Can Problem8
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7.3.5 The Wire-Cutting Problem5
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7.4.1 The Pebble Problem8
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7.4.2 The Ladder Problem6
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7.4.3 The Baseball Problem7
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7.4.4 The Blimp Problem7
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Chapter 7 Practice Test20
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Chapter 7 Test20
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8.1.1 An Introduction to Curve Sketching7
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8.1.2 Three Big Theorems12
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8.2.1 Critical Points5
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8.2.2 Maximum and Minimum13
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8.2.3 Regions Where a Function Increases or Decreases12
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8.2.4 The First Derivative Test5
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8.3.1 Concavity and Inflection Points9
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8.3.2 Using the Second Derivative to Examine Concavity6
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8.4.1 Graphs of Polynomial Functions9
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8.4.2 Cusp Points and the Derivative8
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8.4.3 Domain-Restricted Functions and the Derivative6
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8.4.4 The Second Derivative Test8
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8.5.1 Vertical Asymptotes7
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8.5.2 Horizontal Asymptotes and Infinite Limits9
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8.5.3 Graphing Functions with Asymptotes5
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8.5.4 Functions with Asymptotes and Holes5
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8.5.5 Functions with Asymptotes and Critical Points5
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Chapter 8 Practice Test20
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Chapter 8 Test20
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9.1.1 Antidifferentiation8
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9.1.2 Antiderivatives of Powers of x9
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9.1.3 Antiderivatives of Trigonometric and Exponential Functions11
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9.2.1 Undoing the Chain Rule9
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9.2.2 Integrating Polynomials by Substitution12
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9.3.1 Integrating Composite Trigonometric Functions by Substitution12
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9.3.2 Integrating Composite Exponential and Rational Functions by Substitution10
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9.3.3 More Integrating Tirgonometric Functions by Substitution12
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9.3.4 Choosing Effective Function Decompositions6
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9.4.1 Approximating Areas of Plane Regions5
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9.4.2 Areas, Riemann Sums, and Definite Integrals12
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9.4.3 The Fundamental Theorem of Calculus, Part I12
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9.4.4 The Fundamental Theorem of Calculus, Part II5
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9.4.5 Illustrating the Fundamental Theorem of Calculus10
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9.4.6 Evaluating Definite Integrals13
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9.5.1 An Overview of Trigonometric Substitution Strategy12
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9.5.2 Trigonometric Substitution Involving a Definite Integral: Part One2
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9.5.3 Trigonometric Substitution Involving a Definite Integral: Part Two9
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9.6.1 Deriving the Trapezoidal Rule12
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9.6.2 An Example of the Trapezoidal Rule14
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Chapter 9 Practice Test20
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Chapter 9 Test20
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10.1.1 Antiderivatives and Motion12
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10.1.2 Gravity and Vertical Motion11
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10.1.3 Solving Vertical Motion Problems8
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10.2.1 The Area between Two Curves7
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10.2.2 Limits of Integration and Area7
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10.2.3 Common Mistakes to Avoid When Finding Areas6
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10.2.4 Regions Bound by Several Curves6
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10.3.1 Finding Areas by Integrating with Respect to y: Part One8
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10.3.2 Finding Areas by Integrating with Respect to y: Part Two8
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10.3.3 Area, Integration by Substitution, and Trigonometry8
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10.4.1 Finding the Average Value of a Function8
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10.5.1 Finding Volumes Using Cross-Sectional Slices8
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10.5.2 An Example of Finding Cross-Sectional Volumes8
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10.6.1 Solids of Revolution7
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10.6.2 The Disk Method along the y-Axis9
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10.6.3 A Transcendental Example of the Disk Method8
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10.6.4 The Washer Method across the x-Axis8
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10.6.5 The Washer Method across the y-Axis8
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10.7.1 Introducing the Shell Method8
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10.7.2 Why Shells Can Be Better Than Washers6
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10.7.3 The Shell Method: Integrating with Respect to y6
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10.8.1 An Introduction to Work12
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10.8.2 Calculating Work12
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10.8.3 Hooke's Law12
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10.9.1 Center of Mass9
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10.9.2 The Center of Mass of a Thin Plate11
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10.10.1 An Introduction to Arc Length12
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10.10.2 Finding Arc Lengths of Curves Given by Functions12
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Chapter 10 Practice Test25
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Chapter 10 Test25
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11.1.1 An Introduction to Differential Equations12
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11.1.2 Solving Separable Differential Equations13
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11.1.3 Finding a Particular Solution12
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11.1.4 Direction Fields15
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11.1.5 Euler's Method for Solving Differential Equations Numerically13
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11.2.1 Exponential Growth11
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11.2.2 Logistic Growth13
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11.2.3 Radioactive Decay10
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Chapter 11 Practice Test12
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Chapter 11 Test12
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12.1.1 Indeterminate Forms14
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12.1.2 An Introduction to L'Hôpital's Rule14
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12.1.3 Basic Uses of L'Hôpital's Rule10
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12.1.4 More Exotic Examples of Indeterminate Forms14
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12.2.1 L'Hôpital's Rule and Indeterminate Products10
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12.2.2 L'Hôpital's Rule and Indeterminate Differences14
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12.2.3 L'Hôpital's Rule and One to the Infinite Power7
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12.2.4 Another Example of One to the Infinite Power10
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12.3.1 The First Type of Improper Integral10
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12.3.2 The Second Type of Improper Integral10
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12.3.3 Infinite Limits of Integration, Convergence, and Divergence11
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Chapter 12 Practice Test15
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Chapter 12 Test15
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Practice Final Exam30
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Final Exam30
