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AP Calculus AB

This class was created by Brainscape user Irina Soloshenko. Visit their profile to learn more about the creator.

Flashcard maker: Irina Soloshenko
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Decks in this class (190)

1.1.1 An Introduction to Thinkwell Calculus
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1  cards
1.1.2 The Two Questions of Calculus
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3  cards
1.1.3 Average Rates of Change
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14  cards
1.1.4 How to Do Math
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1  cards
1.2.1 Functions
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16  cards
1.2.2 Graphing Lines
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14  cards
1.2.3 Parabolas
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15  cards
1.2.4 Some Non-Euclidean Geometry
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1  cards
Chapter 1 Practice Test
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20  cards
Chapter 1 Test
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20  cards
2.1.1 Finding Rate of Change over an Interval
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18  cards
2.1.2 Finding Limits Graphically
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9  cards
2.1.3 The Formal Definition of a Limit
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6  cards
2.1.4 The Limit Laws, Part I
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7  cards
2.1.5 The Limit Laws, Part II
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17  cards
2.1.6 One-Sided Limits
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11  cards
2.1.7 The Squeeze Theorem
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13  cards
2.1.8 Continuity and Discontinuity
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13  cards
2.2.1 Evaluating Limits
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17  cards
2.2.2 Limits and Indeterminate Forms
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12  cards
2.2.3 Two Techniques for Evaluating Limits
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7  cards
2.2.4 An Overview of Limits
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11  cards
Chapter 2 Practice Test
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20  cards
Chapter 2 Test
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20  cards
3.1.1 Rates of Change, Secants, and Tangents
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12  cards
3.1.2 Finding Instantaneous Velocity
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14  cards
3.1.3 The Derivative
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13  cards
3.1.4 Differentiability
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9  cards
3.2.1 The Slope of a Tangent Line
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9  cards
3.2.2 Instantaneous Rate
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14  cards
3.2.3 The Equation of a Tangent Line
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17  cards
3.2.4 More on Instantaneous Rate
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8  cards
3.3.1 The Derivative of the Reciprocal Function
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19  cards
3.3.2 The Derivative of the Square Root Function
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16  cards
Chapter 3 Practice Test
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20  cards
Chapter 3 Test
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20  cards
4.1.1 A Shortcut for Finding Derivatives
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14  cards
4.1.2 A Quick Proof of the Power Rule
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12  cards
4.1.3 Uses of the Power Rule
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24  cards
4.2.1 The Product Rule
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12  cards
4.2.2 The Quotient Rule
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9  cards
4.3.1 An Introduction to the Chain Rule
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15  cards
4.3.2 Using the Chain Rule
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14  cards
4.3.3 Combining Computational Techniques
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14  cards
Chapter 4 Practice Test
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20  cards
Chapter 4 Test
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20  cards
5.1.1 A Review of Trigonometry
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13  cards
5.1.2 Graphing Trigonometric Functions
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10  cards
5.1.3 The Derivatives of Trigonometric Functions
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17  cards
5.1.4 The Number Pi
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16  cards
5.2.1 Graphing Exponential Functions
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13  cards
5.2.2 Derivatives of Exponential Functions
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8  cards
5.3.1 Evaluating Logarithmic Functions
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11  cards
5.3.2 The Derivative of the Natural Log Function
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10  cards
5.3.3 Using the Derivative Rules with Transcendental Functions
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8  cards
Chapter 5 Practice Test
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20  cards
Chapter 5 Test
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20  cards
6.1.1 An Introduction to Implicit Differentiation
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13  cards
6.1.2 Finding the Derivative Implicitly
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14  cards
6.2.1 Using Implicit Differentiation
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14  cards
6.2.2 Applying Implicit Differentiation
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9  cards
6.3.1 The Exponential and Natural Log Functions
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12  cards
6.3.2 Differentiating Logarithmic Functions
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12  cards
6.3.3 Logarithmic Differentiation
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14  cards
6.3.4 The Basics of Inverse Functions
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12  cards
6.3.5 Finding the Inverse of a Function
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12  cards
6.4.1 Derivatives of Inverse Function
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12  cards
6.5.1 The Inverse Sine, Cosine, and Tangent Functions
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12  cards
6.5.2 The Inverse Secant, Cosecant, and Cotangent Functions
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12  cards
6.5.3 Evaluating Inverse Trigonometric Functions
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12  cards
6.6.1 Derivatives of Inverse Trigonometric Functions
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12  cards
6.7.1 Defining the Hyperbolic Functions
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12  cards
6.7.2 Hyperbolic Identities
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12  cards
6.7.3 Derivatives of Hyperbolic Functions
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12  cards
Chapter 6 Practice Test
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20  cards
Chapter 6 Test
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20  cards
Practice Midterm Exam
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20  cards
Midterm Exam
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20  cards
7.1.1 Acceleration and the Derivative
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9  cards
7.1.2 Solving Word Problems Involving Distance and Velocity
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15  cards
7.2.1 Higher-Order Derivatives and Linear Approximation
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14  cards
7.2.2 Using the Tangent Line Approximation Formula
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14  cards
7.2.3 Newton's Method
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6  cards
7.3.1 The Connection Between Slope and Optimization
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12  cards
7.3.2 The Fence Problem
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8  cards
7.3.3 The Box Problem
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8  cards
7.3.4 The Can Problem
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8  cards
7.3.5 The Wire-Cutting Problem
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5  cards
7.4.1 The Pebble Problem
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8  cards
7.4.2 The Ladder Problem
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6  cards
7.4.3 The Baseball Problem
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7  cards
7.4.4 The Blimp Problem
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7  cards
Chapter 7 Practice Test
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20  cards
Chapter 7 Test
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20  cards
8.1.1 An Introduction to Curve Sketching
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7  cards
8.1.2 Three Big Theorems
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12  cards
8.2.1 Critical Points
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5  cards
8.2.2 Maximum and Minimum
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13  cards
8.2.3 Regions Where a Function Increases or Decreases
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12  cards
8.2.4 The First Derivative Test
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5  cards
8.3.1 Concavity and Inflection Points
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9  cards
8.3.2 Using the Second Derivative to Examine Concavity
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6  cards
8.4.1 Graphs of Polynomial Functions
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9  cards
8.4.2 Cusp Points and the Derivative
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8  cards
8.4.3 Domain-Restricted Functions and the Derivative
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6  cards
8.4.4 The Second Derivative Test
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8  cards
8.5.1 Vertical Asymptotes
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7  cards
8.5.2 Horizontal Asymptotes and Infinite Limits
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9  cards
8.5.3 Graphing Functions with Asymptotes
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5  cards
8.5.4 Functions with Asymptotes and Holes
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5  cards
8.5.5 Functions with Asymptotes and Critical Points
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5  cards
Chapter 8 Practice Test
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20  cards
Chapter 8 Test
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20  cards
9.1.1 Antidifferentiation
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8  cards
9.1.2 Antiderivatives of Powers of x
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9  cards
9.1.3 Antiderivatives of Trigonometric and Exponential Functions
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11  cards
9.2.1 Undoing the Chain Rule
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9  cards
9.2.2 Integrating Polynomials by Substitution
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12  cards
9.3.1 Integrating Composite Trigonometric Functions by Substitution
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12  cards
9.3.2 Integrating Composite Exponential and Rational Functions by Substitution
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10  cards
9.3.3 More Integrating Tirgonometric Functions by Substitution
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12  cards
9.3.4 Choosing Effective Function Decompositions
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6  cards
9.4.1 Approximating Areas of Plane Regions
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5  cards
9.4.2 Areas, Riemann Sums, and Definite Integrals
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12  cards
9.4.3 The Fundamental Theorem of Calculus, Part I
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12  cards
9.4.4 The Fundamental Theorem of Calculus, Part II
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5  cards
9.4.5 Illustrating the Fundamental Theorem of Calculus
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10  cards
9.4.6 Evaluating Definite Integrals
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13  cards
9.5.1 An Overview of Trigonometric Substitution Strategy
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12  cards
9.5.2 Trigonometric Substitution Involving a Definite Integral: Part One
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2  cards
9.5.3 Trigonometric Substitution Involving a Definite Integral: Part Two
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9  cards
9.6.1 Deriving the Trapezoidal Rule
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12  cards
9.6.2 An Example of the Trapezoidal Rule
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14  cards
Chapter 9 Practice Test
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20  cards
Chapter 9 Test
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20  cards
10.1.1 Antiderivatives and Motion
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12  cards
10.1.2 Gravity and Vertical Motion
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11  cards
10.1.3 Solving Vertical Motion Problems
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8  cards
10.2.1 The Area between Two Curves
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7  cards
10.2.2 Limits of Integration and Area
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7  cards
10.2.3 Common Mistakes to Avoid When Finding Areas
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6  cards
10.2.4 Regions Bound by Several Curves
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6  cards
10.3.1 Finding Areas by Integrating with Respect to y: Part One
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8  cards
10.3.2 Finding Areas by Integrating with Respect to y: Part Two
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8  cards
10.3.3 Area, Integration by Substitution, and Trigonometry
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8  cards
10.4.1 Finding the Average Value of a Function
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8  cards
10.5.1 Finding Volumes Using Cross-Sectional Slices
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8  cards
10.5.2 An Example of Finding Cross-Sectional Volumes
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8  cards
10.6.1 Solids of Revolution
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7  cards
10.6.2 The Disk Method along the y-Axis
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9  cards
10.6.3 A Transcendental Example of the Disk Method
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8  cards
10.6.4 The Washer Method across the x-Axis
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8  cards
10.6.5 The Washer Method across the y-Axis
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8  cards
10.7.1 Introducing the Shell Method
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8  cards
10.7.2 Why Shells Can Be Better Than Washers
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6  cards
10.7.3 The Shell Method: Integrating with Respect to y
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6  cards
10.8.1 An Introduction to Work
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12  cards
10.8.2 Calculating Work
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12  cards
10.8.3 Hooke's Law
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12  cards
10.9.1 Center of Mass
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9  cards
10.9.2 The Center of Mass of a Thin Plate
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11  cards
10.10.1 An Introduction to Arc Length
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12  cards
10.10.2 Finding Arc Lengths of Curves Given by Functions
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12  cards
Chapter 10 Practice Test
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25  cards
Chapter 10 Test
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25  cards
11.1.1 An Introduction to Differential Equations
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12  cards
11.1.2 Solving Separable Differential Equations
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13  cards
11.1.3 Finding a Particular Solution
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12  cards
11.1.4 Direction Fields
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15  cards
11.1.5 Euler's Method for Solving Differential Equations Numerically
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13  cards
11.2.1 Exponential Growth
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11  cards
11.2.2 Logistic Growth
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13  cards
11.2.3 Radioactive Decay
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10  cards
Chapter 11 Practice Test
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12  cards
Chapter 11 Test
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12  cards
12.1.1 Indeterminate Forms
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14  cards
12.1.2 An Introduction to L'Hôpital's Rule
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14  cards
12.1.3 Basic Uses of L'Hôpital's Rule
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10  cards
12.1.4 More Exotic Examples of Indeterminate Forms
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14  cards
12.2.1 L'Hôpital's Rule and Indeterminate Products
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10  cards
12.2.2 L'Hôpital's Rule and Indeterminate Differences
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14  cards
12.2.3 L'Hôpital's Rule and One to the Infinite Power
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7  cards
12.2.4 Another Example of One to the Infinite Power
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10  cards
12.3.1 The First Type of Improper Integral
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10  cards
12.3.2 The Second Type of Improper Integral
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10  cards
12.3.3 Infinite Limits of Integration, Convergence, and Divergence
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11  cards
Chapter 12 Practice Test
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15  cards
Chapter 12 Test
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15  cards
Practice Final Exam
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30  cards
Final Exam
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30  cards

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AP Calculus AB

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