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Part I Using This Book to Improve Your AP Score |
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1 | (6) |
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Preview: Your Knowledge, Your Expectations |
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2 | (1) |
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Your Guide to Using This Book |
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2 | (1) |
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3 | (4) |
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7 | (52) |
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9 | (28) |
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Practice Test 1 Diagnostic Answer Key and Explanations |
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37 | (21) |
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How to Score Practice Test 1 |
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58 | (1) |
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Part III About the AP Calculus AB Exam |
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59 | (8) |
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AB Calculus vs. BC Calculus |
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60 | (1) |
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The Structure of the AP Calculus AB Exam |
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60 | (1) |
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How the AP Calculus AB Exam is Scored |
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61 | (1) |
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Past AP Calculus AB Score Distributions |
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61 | (1) |
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Overview of Content Topics |
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62 | (2) |
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General Overview of This Book |
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64 | (1) |
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65 | (1) |
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66 | (1) |
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Designing Your Study Plan |
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66 | (1) |
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Part IV Test-Taking Strategies for the AP Calculus AB Exam |
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67 | (10) |
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1 How to Approach Multiple-Choice Questions |
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69 | (4) |
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2 How to Approach Free-Response Questions |
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73 | (4) |
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Part V Content Review for the AP Calculus AB Exam |
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77 | (432) |
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79 | (32) |
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Introducing Calculus: Can Change Occur at an Instant? |
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80 | (1) |
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Defining Limits and Using Limit Notation |
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80 | (2) |
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Estimating Limit Values from Graphs |
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82 | (1) |
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Estimating Limit Values from Tables |
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83 | (1) |
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Determining Limits Using Algebraic Properties of Limits |
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84 | (1) |
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Determining Limits Using Algebraic Manipulation |
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85 | (2) |
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Selecting Procedures for Determining Limits |
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87 | (4) |
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Determining Limits Using the Squeeze Theorem |
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91 | (2) |
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Connecting Multiple Representations of Limits |
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93 | (2) |
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Exploring Types of Discontinuities |
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95 | (4) |
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Defining Continuity at a Point |
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99 | (2) |
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Confirming Continuity Over an Interval |
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101 | (1) |
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102 | (1) |
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Connecting Infinite Limits and Vertical Asymptotes |
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103 | (2) |
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Connecting Limits at Infinity and Horizontal Asymptotes |
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105 | (1) |
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Working with the Intermediate Value Theorem (IVT) |
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106 | (3) |
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109 | (2) |
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4 Differentiation: Definition and Basic Derivative Rules |
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111 | (28) |
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Defining Average and Instantaneous Rates of Change at a Point |
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112 | (1) |
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Defining the Derivative of a Function and Using Derivative Notation |
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113 | (6) |
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Estimating Derivatives of a Function at a Point |
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119 | (3) |
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Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist |
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122 | (1) |
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123 | (1) |
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Derivative Rules: Constant, Sum, Difference, and Constant Multiple |
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124 | (2) |
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Derivatives of cos x, sin x, ex and In x |
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126 | (7) |
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133 | (1) |
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134 | (1) |
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Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions |
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135 | (3) |
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138 | (1) |
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5 Differentiation: Composite, Implicit, and Inverse Functions |
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139 | (24) |
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140 | (4) |
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144 | (6) |
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Differentiating Inverse Functions |
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150 | (4) |
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Differentiating Inverse Trigonometric Functions |
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154 | (2) |
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Selecting Procedures for Calculating Derivatives |
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156 | (2) |
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Calculating Higher-Order Derivatives |
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158 | (3) |
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161 | (2) |
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6 Contextual Applications of Differentiation |
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163 | (30) |
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Interpreting the Meaning of the Derivative in Context |
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164 | (1) |
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Straight-Line Motion: Connecting Position, Velocity, and Acceleration |
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164 | (6) |
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Rates of Change in Applied Contexts Other Than Motion |
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170 | (1) |
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Introduction to Related Rates |
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170 | (1) |
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Solving Related Rates Problems |
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171 | (6) |
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Approximating Values of a Function Using Local Linearity and Linearization |
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177 | (10) |
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Using L'Hospital's Rule for Determining Limits of Indeterminate Forms |
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187 | (5) |
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192 | (1) |
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7 Analytical Applications of Differentiation |
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193 | (52) |
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Using the Mean Value Theorem |
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194 | (5) |
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Extreme Value Theorem, Global Versus Local Extrema, and Critical Points |
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199 | (1) |
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Determining Intervals on Which a Function Is Increasing or Decreasing |
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200 | (2) |
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Using the First Derivative Test to Determine Relative (Local) Extrema |
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202 | (2) |
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Using the Candidates Test to Determine Absolute (Global) Extrema |
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204 | (2) |
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Determining Concavity of Functions over Their Domains |
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206 | (3) |
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Using the Second Derivative Test to Determine Extrema |
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209 | (3) |
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Sketching Graphs of Functions and Their Derivatives |
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212 | (15) |
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Connecting a Function, Its First Derivative, and Its Second Derivative |
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227 | (5) |
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Introduction to Optimization Problems |
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232 | (1) |
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Solving Optimization Problems |
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233 | (10) |
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Exploring Behaviors and Implicit Relations |
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243 | (1) |
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244 | (1) |
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8 Integration and Accumulation of Change |
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245 | (64) |
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Exploring Accumulations of Change |
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246 | (1) |
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Approximating Areas with Riemann Sums |
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247 | (13) |
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Riemann Sums, Summation Notation, and Definite Integral Notation |
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260 | (1) |
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The Fundamental Theorem of Calculus and Accumulation Functions |
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261 | (2) |
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Interpreting the Behavior of Accumulation Functions Involving Area |
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263 | (4) |
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Applying Properties of Definite Integrals |
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267 | (1) |
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The Fundamental Theorem of Calculus and Definite Integrals |
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268 | (1) |
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Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation |
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269 | (9) |
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Integrating Using Substitution |
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278 | (23) |
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Integrating Functions Using Long Division and Completing the Square |
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301 | (4) |
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Selecting Techniques for Antidifferentiation |
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305 | (2) |
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307 | (2) |
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309 | (18) |
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Modeling Situations with Differential Equations |
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310 | (1) |
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Verifying Solutions for Differential Equations |
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310 | (1) |
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311 | (4) |
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Reasoning Using Slope Fields |
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315 | (2) |
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Finding General Solutions Using Separation of Variables |
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317 | (1) |
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Finding Particular Solutions Using Initial Conditions and Separation of Variables |
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318 | (4) |
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Exponential Models with Differential Equations |
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322 | (4) |
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326 | (1) |
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10 Applications of Integration |
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327 | (26) |
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Finding the Average Value of a Function on an Interval |
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328 | (2) |
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Connecting Position, Velocity, and Acceleration of Functions Using Integrals |
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330 | (1) |
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Using Accumulation Functions and Definite Integrals in Applied Contexts |
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331 | (1) |
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Finding the Area Between Curves Expressed as Functions of x |
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332 | (2) |
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Finding the Area Between Curves Expressed as Functions of y |
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334 | (3) |
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Finding the Area Between Curves That Intersect at More than Two Points |
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337 | (1) |
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Volumes with Cross Sections: Squares and Rectangles |
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338 | (2) |
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Volumes with Cross Sections: Triangles and Semicircles |
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340 | (1) |
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Volume with Disc Method: Revolving Around x- or y-Axis |
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341 | (3) |
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Volume with Disc Method: Revolving Around Other Axes |
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344 | (1) |
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Volume with Washer Method: Revolving Around x- or y-Axis |
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345 | (3) |
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Volume with Washer Method: Revolving Around Other Axes |
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348 | (3) |
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351 | (2) |
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11 Answers to Practice Problems Sets |
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353 | (130) |
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12 Answers to End of
Chapter Drills |
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483 | (26) |
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Part VI Practice Tests 2 and 3 |
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509 | (108) |
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511 | (28) |
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Practice Test 2 Answers and Explanations |
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539 | (24) |
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How to Score Practice Test 2 |
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563 | (2) |
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565 | (28) |
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Practice Test 3 Answers and Explanations |
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593 | (22) |
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How to Score Practice Test 3 |
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615 | (2) |
| About the Author |
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617 | |
