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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 | (60) |
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9 | (30) |
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Practice Test 1 Diagnostic Answer Key and Explanations |
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39 | (26) |
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How to Score Practice Test 1 |
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65 | (2) |
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Part III About the AP Calculus BC Exam |
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67 | (10) |
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AB Calculus vs. BC Calculus |
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68 | (1) |
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Structure of the AP Calculus BC Exam |
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68 | (1) |
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How the AP Calculus BC Exam is Scored |
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69 | (1) |
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Past AP Calculus BC Score Distributions |
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69 | (1) |
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Overview of Content Topics |
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70 | (3) |
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General Overview of This Book |
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73 | (1) |
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74 | (1) |
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75 | (1) |
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Designing Your Study Plan |
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75 | (2) |
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Part IV Test-Taking Strategies for the AP Calculus BC Exam |
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77 | (10) |
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1 How to Approach Multiple-Choice Questions |
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79 | (4) |
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2 How to Approach Free-Response Questions |
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83 | (4) |
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Part V Content Review for the AP Calculus BC Exam |
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87 | (548) |
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89 | (32) |
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Introducing Calculus: Can Change Occur at an Instant? |
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90 | (1) |
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Defining Limits and Using Limit Notation |
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90 | (2) |
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Estimating Limit Values from Graphs |
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92 | (1) |
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Estimating Limit Values from Tables |
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93 | (1) |
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Determining Limits Using Algebraic Properties of Limits |
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94 | (1) |
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Determining Limits Using Algebraic Manipulation |
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95 | (2) |
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Selecting Procedures for Determining Limits |
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97 | (4) |
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Determining Limits Using the Squeeze Theorem |
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101 | (2) |
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Connecting Multiple Representations of Limits |
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103 | (2) |
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Exploring Types of Discontinuities |
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105 | (4) |
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Defining Continuity at a Point |
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109 | (2) |
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Confirming Continuity over an Interval |
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111 | (1) |
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112 | (1) |
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Connecting Infinite Limits and Vertical Asymptotes |
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113 | (2) |
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Connecting Limits at Infinity and Horizontal Asymptotes |
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115 | (1) |
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Working with the Intermediate Value Theorem (IVT) |
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116 | (3) |
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119 | (2) |
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4 Differentiation: Definition and Basic Derivative Rules |
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121 | (28) |
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Defining Average and Instantaneous Rates of Change at a Point |
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122 | (1) |
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Defining the Derivative of a Function and Using Derivative Notation |
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123 | (6) |
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Estimating Derivatives of a Function at a Point |
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129 | (3) |
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Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist |
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132 | (1) |
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133 | (1) |
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Derivative Rules: Constant, Sum, Difference, and Constant Multiple |
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134 | (2) |
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Derivatives of cos x, sin x, ex, and In x |
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136 | (7) |
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143 | (1) |
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144 | (1) |
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Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions |
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145 | (3) |
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148 | (1) |
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5 Differentiation: Composite, Implicit, and Inverse Functions |
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149 | (24) |
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150 | (4) |
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154 | (6) |
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Differentiating Inverse Functions |
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160 | (4) |
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Differentiating Inverse Trigonometric Functions |
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164 | (2) |
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Selecting Procedures for Calculating Derivatives |
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166 | (2) |
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Calculating Higher-Order Derivatives |
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168 | (3) |
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171 | (2) |
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6 Contextual Applications of Differentiation |
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173 | (30) |
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Interpreting the Meaning of the Derivative in Context |
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174 | (1) |
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Straight-Line Motion: Connecting Position, Velocity, and Acceleration |
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174 | (6) |
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Rates of Change in Applied Contexts Other Than Motion |
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180 | (1) |
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Introduction to Related Rates |
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180 | (1) |
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Solving Related Rates Problems |
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181 | (6) |
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Approximating Values of a Function Using Local Linearity and Linearization |
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187 | (10) |
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Using L'Hospital's Rule for Determining Limits of Indeterminate Forms |
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197 | (5) |
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202 | (1) |
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7 Analytical Applications of Differentiation |
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203 | (54) |
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Using the Mean Value Theorem |
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204 | (5) |
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Extreme Value Theorem, Global Versus Local Extrema, and Critical Points |
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209 | (1) |
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Determining Intervals on Which a Function Is Increasing or Decreasing |
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210 | (2) |
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Using the First Derivative Test to Determine Relative (Local) Extrema |
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212 | (2) |
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Using the Candidates Test to Determine Absolute (Global) Extrema |
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214 | (2) |
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Determining Concavity of Functions over Their Domains |
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216 | (3) |
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Using the Second Derivative Test to Determine Extrema |
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219 | (3) |
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Sketching Graphs of Function and Their Derivatives |
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222 | (15) |
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Connecting a Function, Its First Derivative, and Its Second Derivative |
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237 | (6) |
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Introduction to Optimization Problems |
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243 | (1) |
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Solving Optimization Problems |
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244 | (10) |
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Exploring Behaviors of Implicit Relations |
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254 | (1) |
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255 | (2) |
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8 Integration and Accumulation of Change |
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257 | (78) |
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Exploring Accumulations of Change |
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258 | (1) |
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Approximating Areas with Riemann Sums |
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259 | (13) |
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Riemann Sums, Summation Notation, and Definite Integral Notation |
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272 | (1) |
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The Fundamental Theorem of Calculus and Accumulation Functions |
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273 | (2) |
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Interpreting the Behavior of Accumulation Functions Involving Area |
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275 | (4) |
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Applying Properties of Definite Integrals |
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279 | (1) |
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The Fundamental Theorem of Calculus and Definite Integrals |
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280 | (1) |
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Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation |
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281 | (9) |
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Integrating Using Substitution |
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290 | (23) |
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Integrating Functions Using Long Division and Completing the Square |
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313 | (4) |
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Integration Using Integration by Parts |
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317 | (6) |
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Using Linear Partial Fractions |
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323 | (3) |
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Evaluating Improper Integrals |
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326 | (4) |
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Selecting Techniques for Antidifferentiation |
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330 | (2) |
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332 | (3) |
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335 | (26) |
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Modeling Situations with Differential Equations |
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336 | (1) |
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Verifying Solutions for Differential Equations |
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336 | (1) |
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337 | (4) |
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Reasoning Using Slope Fields |
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341 | (2) |
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Approximating Solutions Using Euler's Method |
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343 | (6) |
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Finding General Solutions Using Separation of Variables |
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349 | (1) |
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Finding Particular Solutions Using Initial Conditions and Separation of Variables |
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350 | (4) |
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Exponential Models with Differential Equations |
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354 | (2) |
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Logistic Models with Differential Equations |
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356 | (4) |
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360 | (1) |
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10 Applications of Integration |
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361 | (30) |
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Finding the Average Value of a Function on an Interval |
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362 | (2) |
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Connecting Position, Velocity, and Acceleration Functions Using Integrals |
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364 | (1) |
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Using Accumulation Functions and Definite Integrals in Applied Contexts |
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365 | (1) |
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Finding the Area Between Curves Expressed as Functions of x |
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366 | (2) |
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Finding the Area Between Curves Expressed as Functions of y |
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368 | (3) |
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Finding the Area Between Curves That Intersect at More Than Two Points |
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371 | (1) |
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Volumes with Cross-Sections: Squares and Rectangles |
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372 | (2) |
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Volumes with Cross-Sections: Triangles and Semicircles |
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374 | (1) |
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Volume with Disc Method: Revolving Around the x- or y-Axis |
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375 | (3) |
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Volume with Disc Method: Revolving Around Other Axes |
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378 | (1) |
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Volume with Washer Method: Revolving Around the x- or y-Axis |
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379 | (3) |
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Volume with Washer Method: Revolving Around Other Axes |
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382 | (3) |
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The Arc Length of a Smooth, Planar Curve and Distance Traveled |
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385 | (3) |
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388 | (3) |
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11 Parametric Equations, Polar Coordinates, and Vector-Valued Functions |
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391 | (18) |
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Defining and Differentiating Parametric Equations |
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392 | (2) |
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Second Derivatives of Parametric Equations |
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394 | (1) |
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Finding Arc Lengths of Curves Given by Parametric Equations |
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395 | (2) |
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Defining and Differentiating Vector-Valued Functions |
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397 | (1) |
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Integrating Vector-Valued Functions |
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398 | (2) |
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Solving Motion Problems Using Parametric and Vector-Valued Functions |
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400 | (2) |
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Defining Polar Coordinates and Differentiating in Polar Form |
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402 | (1) |
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Finding the Area of a Polar Region or the Area Bounded by a Single Polar Curve |
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403 | (2) |
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Finding the Area of the Region Bounded by Two Polar Curves |
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405 | (2) |
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407 | (2) |
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12 Infinite Sequences and Series |
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409 | (30) |
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Defining Convergent and Divergent Infinite Series |
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410 | (3) |
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Working with Geometric Series |
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413 | (2) |
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The nth Term Test for Divergence |
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415 | (1) |
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Integral Test for Convergence |
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416 | (1) |
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Harmonic Series and p-Series |
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417 | (2) |
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Comparison Tests for Convergence |
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419 | (3) |
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Alternating Series Test for Convergence |
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422 | (1) |
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Ratio Test for Convergence |
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423 | (1) |
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Determining Absolute or Conditional Convergence |
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424 | (1) |
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Alternating Series Error Bound |
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425 | (1) |
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Finding Taylor Polynomial Approximations of Functions |
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426 | (2) |
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428 | (1) |
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Radius and Interval of Convergence of Power Series |
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429 | (1) |
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Finding Taylor or Maclaurin Series for a Function |
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430 | (2) |
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Representing Functions as Power Series |
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432 | (5) |
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437 | (2) |
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13 Answers to Practice Problem Sets |
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439 | (162) |
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14 Answers to End of
Chapter Drills |
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601 | (34) |
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Part VI Practice Tests 2 and 3 |
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635 | (110) |
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637 | (30) |
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16 Practice Test 2: Answers and Explanations |
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667 | (26) |
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How to Score Practice Test 2 |
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691 | (2) |
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693 | (32) |
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18 Practice Test 3: Answers and Explanations |
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725 | (20) |
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How to Score Practice Test 3 |
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743 | (2) |
| About the Author |
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745 | |
