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| Acknowledgments | |
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| Before You Begin | |
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| How This Book Is Organized | |
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| Special Study Features | |
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| Appendix | |
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| You're Well on Your Way to Success | |
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| Give Us Your Feedback | |
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| Mike Kelley's How to Use This Book | |
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| Quick Reference Guide | |
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| Top 10 Strategies to Raise Your Score | |
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| AP Calculus AB & BC Basics | |
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| All About the AP Calculus AB & BC Tests | |
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| Frequently Asked Questions About the AP Calculus Tests | |
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| Summing It Up | |
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| AP Calculus AP & BC Review | |
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| Calculus Prerequisites | |
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| Functions and Relations | |
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| Answers and Explanations | |
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| Function Properties | |
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| Answers and Explanations | |
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| Inverse Functions | |
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| Answers and Explanations | |
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| Hands-On Activity 2.1: Transforming Functions | |
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| Selected Solutions to Hands-on Activity 2.1 | |
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| Answers and Explanations | |
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| Trigonometry | |
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| Answers and Explanations | |
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| Parametric Equations (BC Topic Only) | |
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| Answers and Explanations | |
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| Polar Equations (BC Topic Only) | |
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| Answers and Explanations | |
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| Vectors and Vector Equations (BC Topic Only) | |
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| Answers and Explanations | |
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| Technology: Solving Equations with a Graphing Calculator | |
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| Answers and Explanations | |
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| Summing It Up | |
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| Limits and Continuity | |
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| Hands-On Activity 3.1: What Is a Limit? | |
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| Selected Solutions to Hands-On Activity 3.1 | |
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| Answers and Explanations | |
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| Evaluating Limits Analytically | |
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| Answers and Explanations | |
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| Continuity | |
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| Answers and Explanations | |
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| Hands-On Activity 3.2: The Extreme Value Theorem | |
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| Selected Solutions to Hands-On Activity 3.2 | |
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| Answers and Explanations | |
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| Hands-On Activity 3.3: The Intermediate Value Theorem | |
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| Solutions to Hands-On Activity 3.3 | |
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| Answers and Explanations | |
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| Limits Involving Infinity | |
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| Answers and Explanations | |
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| Special Limits | |
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| Answers and Explanations | |
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| Technology: Evaluating Limits with a Graphing Calculator | |
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| Answers and Explanations | |
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| Summing It Up | |
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| Differentiating | |
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| Derivative as a Rate of Change | |
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| Answers and Explanations | |
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| The Power Rule | |
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| Answers and Explanations | |
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| Derivatives to Memorize | |
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| Answers and Explanations | |
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| The Chain Rule | |
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| Answers and Explanations | |
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| The Product Rule | |
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| Answers and Explanations | |
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| The Quotient Rule | |
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| Answers and Explanations | |
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| A Word About Respecting Variables | |
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| Answers and Explanations | |
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| Implicit Differentiation | |
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| Answers and Explanations | |
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| Hands-On Activity 4.1: Approximating Derivatives | |
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| Selected Solutions to Hands-On Activity 4.1 | |
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| Answers and Explanations | |
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| Technology: Finding Numerical Derivatives with the Graphing Calculator | |
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| Answers and Explanations | |
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| Summing It Up | |
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| Advanced Topics in Differentiation | |
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| The Derivative of an Inverse Function | |
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| Answers and Explanations | |
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| Hands-On Activity 5.1: Linear Approximations | |
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| Solutions to Hands-On Activity 5.1 | |
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| Answers and Explanations | |
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| L'Hopital's Rule (BC Topic Only) | |
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| Answers and Explanations | |
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| Parametric Derivatives (BC Topic Only) | |
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| Answers and Explanations | |
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| Polar Derivatives (BC Topic Only) | |
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| Answers and Explanations | |
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| Technology: Finding Polar and Parametric Derivatives with Your Calculator (BC Topic Only) | |
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| Answers and Explanations | |
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| Summing It Up | |
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| Applications of the Derivative | |
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| Related Rates | |
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| Answers and Explanations | |
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| Hands-On Activity 6.1: Rolle's and Mean Value Theorems | |
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| Selected Solutions to Hands-On Activity 6.1 | |
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| Answers and Explanations | |
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| Hands-On Activity 6.2: The First Derivative Test | |
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| Selected Solutions to Hands-On Activity 6.2 | |
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| Answers and Explanations | |
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| Concavity | |
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| Answers and Explanations | |
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| Motion | |
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| Answers and Explanations | |
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| Motion in the Plane (BC Topic Only) | |
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| Answers and Explanations | |
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| Optimization | |
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| Answers and Explanations | |
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| Technology: Modeling a Particle's Movement with a Graphing Calculator | |
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| Answers and Explanations | |
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| Summing It Up | |
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| Integration | |
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| Basic Antiderivatives | |
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| Answers and Explanations | |
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| Hands-On Activity 7.1: Approximating Area with Riemann Sums | |
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| Selected Solutions to Hands-On Activity 7.1 | |
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| Answers and Explanations | |
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| The Trapezoidal Rule | |
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| Answers and Explanations | |
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| The Fundamental Theorem of Calculus | |
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| Answers and Explanations | |
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| Hands-On Activity 7.2: Accumulation Functions | |
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| Solutions to Hands-On Activity 7.2 | |
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| Answers and Explanations | |
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| The Mean Value Theorem for Integration, Average Value of a Function | |
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| Answers and Explanations | |
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| U-Substitution | |
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| Answers and Explanations | |
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| Integrating Inverse Trigonometrie Functions | |
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| Answers and Explanations | |
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| Technology: Evaluating Definite Integrals with Your Graphing Calculator | |
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| Answers and Explanations | |
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| Summing It Up | |
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| Advanced Methods of Integration | |
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| Miscellaneous Methods of Integration | |
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| Answers and Explanations | |
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| Parts (BC Topic Only) | |
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| Answers and Explanations | |
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| Powers of Trigonometrie Functions (BC Topic Only) | |
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| Answers and Explanations | |
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| Partial Fractions (BC Topic Only) | |
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| Answers and Explanations | |
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| Improper Integrals (BC Topic Only) | |
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| Answers and Explanations | |
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| Technology: Drawing Derivative and Integral Graphs with Your Calculator | |
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| Answers and Explanations | |
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| Summing It Up | |
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| Applications of Integration | |
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| Hands-On Activity 9.1: Area Between Curves | |
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| Selected Solutions to Hands-On Activity 9.1 | |
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| Answers and Explanations | |
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| The Disk and Washer Methods | |
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| Answers and Explanations | |
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| The Shell Method | |
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| Answers and Explanations | |
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| Finding the Volume of Regions with Known Cross Sections | |
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| Answers and Explanations | |
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| Arc Length (BC Topic Only) | |
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| Answers and Explanations | |
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| Polar Area (BC Topic Only) | |
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| Answers and Explanations | |
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| Technology: Using Your Calculator Efficiently | |
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| Answers and Explanations | |
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| Summing It Up | |
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| Differential Equations | |
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| Hands-On Activity 10.1: Separation of Variables | |
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| Solutions to Hands-On Activity 10.1 | |
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| Answers and Explanations | |
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| Hands-On Activity 10.2: Slope Fields | |
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| Selected Solutions to Hands-On Activity 10.2 | |
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| Answers and Explanations | |
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| Euler's Method (BC Topic Only) | |
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| Answers and Explanations | |
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| Exponential Growth and Decay | |
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| Answers and Explanations | |
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| Logistic Growth (BC Topic Only) | |
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| Answers and Explanations | |
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| Technology: A Differential Equations Calculator Program | |
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| Answers and Explanations | |
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| Summing It Up | |
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| Sequences and Series (BC Topics Only) | |
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| Introduction to Sequences and Series, Nth Term Divergence Test | |
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| Answers and Explanations | |
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| Convergence Tests for Infinite Series | |
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| Answers and Explanations | |
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| Power Series | |
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| Answers and Explanations | |
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| Taylor and Maclaurin Series | |
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| Answers and Explanations | |
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| Technology: Viewing and Calculating Sequences and Series with a Graphing Calculator | |
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| Answers and Explanations | |
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| Summing It Up | |
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| Four Practice Tests | |
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| AP Calculus AB | |
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| Section I, Part A | |
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| Section I, Part B | |
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| Section II, Part A | |
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| Section II, Part B | |
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| Answer Key and Explanations | |
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| AP Calculus AB | |
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| Section I, Part A | |
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| Section I, Part B | |
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| Section II, Part A | |
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| Section II, Part B | |
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| Answer Key and Explanations | |
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| AP Calculus BC | |
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| Section I, Part A | |
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| Section I, Part B | |
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| Section II, Part A | |
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| Section II, Part B | |
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| Answer Key and Explanations | |
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| AP Calculus BC | |
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| Section I, Part A | |
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| Section I, Part B | |
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| Section II, Part A | |
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| Section II, Part B | |
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| Answer Key and Explanations | |
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| College-by-College Guide to AP Credit and Placement | |