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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 | |