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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 | (56) |
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9 | (30) |
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Practice Test 1: Answers and Explanations |
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39 | (24) |
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Part III About the AP Calculus BC Exam |
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63 | (10) |
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AB Calculus vs. BC Calculus |
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64 | (1) |
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64 | (1) |
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How the AP Calculus BC Exam is Scored |
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65 | (1) |
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Overview of Content Topics |
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66 | (3) |
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General Overview of This Book |
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69 | (1) |
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70 | (1) |
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71 | (1) |
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Designing Your Study Plan |
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71 | (2) |
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Part IV Test-Taking Strategies for the AP Calculus BC Exam |
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73 | (10) |
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1 How To Approach Multiple-Choice Questions |
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75 | (4) |
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2 How To Approach Free-Response Questions |
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79 | (4) |
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Part V Content Review for the AP Calculus BC Exam |
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83 | (544) |
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85 | (32) |
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Introducing Calculus: Can Change Occur at an Instant? |
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86 | (1) |
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Defining Limits and Using Limit Notation |
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86 | (2) |
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Estimating Limit Values from Graphs |
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88 | (1) |
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Estimating Limit Values from Tables |
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89 | (1) |
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Determining Limits Using Algebraic Properties of Limits |
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90 | (1) |
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Determining Limits Using Algebraic Manipulation |
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91 | (2) |
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Selecting Procedures for Determining Limits |
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93 | (4) |
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Determining Limits Using the Squeeze Theorem |
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97 | (2) |
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Connecting Multiple Representations of Limits |
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99 | (2) |
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Exploring Types of Discontinuities |
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101 | (4) |
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Defining Continuity at a Point |
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105 | (2) |
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Confirming Continuity over an Interval |
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107 | (1) |
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108 | (1) |
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Connecting Infinite Limits and Vertical Asymptotes |
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109 | (2) |
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Connecting Limits at Infinity and Horizontal Asymptotes |
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111 | (1) |
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Working with the Intermediate Value Theorem (IVT) |
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112 | (3) |
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115 | (2) |
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4 Differentiation: Definition And Basic Derivative Rules |
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117 | (28) |
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Defining Average and Instantaneous Rates of Change at a Point |
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118 | (1) |
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Defining the Derivative of a Function and Using Derivative Notation |
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119 | (6) |
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Estimating Derivatives of a Function at a Point |
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125 | (3) |
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Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist |
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128 | (1) |
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129 | (1) |
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Derivative Rules: Constant, Sum, Difference, and Constant Multiple |
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130 | (2) |
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Derivatives of cos x, sin x, ex, and In x |
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132 | (7) |
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139 | (1) |
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140 | (1) |
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Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions |
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141 | (3) |
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144 | (1) |
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5 Differentiation: Composite, Implicit, And Inverse Functions |
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145 | (24) |
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146 | (4) |
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150 | (6) |
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Differentiating Inverse Functions |
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156 | (4) |
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Differentiating Inverse Trigonometric Functions |
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160 | (2) |
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Selecting Procedures for Calculating Derivatives |
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162 | (2) |
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Calculating Higher-Order Derivatives |
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164 | (3) |
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167 | (2) |
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6 Contextual Applications Of Differentiation |
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169 | (30) |
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Interpreting the Meaning of the Derivative in Context |
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170 | (1) |
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Straight-Line Motion: Connecting Position, Velocity, and Acceleration |
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170 | (6) |
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Rates of Change in Applied Contexts Other Than Motion |
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176 | (1) |
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Introduction to Related Rates |
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176 | (1) |
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Solving Related Rates Problems |
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177 | (6) |
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Approximating Values of a Function Using Local Linearity and Linearization |
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183 | (10) |
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Using L'Hospital's Rule for Determining Limits of Indeterminate Forms |
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193 | (5) |
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198 | (1) |
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7 Analytical Applications Of Differentiation |
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199 | (54) |
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Using the Mean Value Theorem |
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200 | (5) |
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Extreme Value Theorem, Global Versus Local Extrema, and Critical Points |
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205 | (1) |
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Determining Intervals on Which a Function Is Increasing or Decreasing |
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206 | (2) |
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Using the First Derivative Test to Determine Relative (Local) Extrema |
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208 | (2) |
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Using the Candidates Test to Determine Absolute (Global) Extrema |
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210 | (2) |
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Determining Concavity of Functions over Their Domains |
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212 | (3) |
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Using the Second Derivative Test to Determine Extrema |
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215 | (3) |
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Sketching Graphs of Function and Their Derivatives |
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218 | (15) |
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Connecting a Function, Its First Derivative, and Its Second Derivative |
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233 | (6) |
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Introduction to Optimization Problems |
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239 | (1) |
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Solving Optimization Problems |
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240 | (10) |
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Exploring Behaviors of Implicit Relations |
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250 | (1) |
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251 | (2) |
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8 Integration And Accumulation Of Change |
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253 | (78) |
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Exploring Accumulations of Change |
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254 | (1) |
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Approximating Areas with Riemann Sums |
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255 | (13) |
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Riemann Sums, Summation Notation, and Definite Integral Notation |
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268 | (1) |
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The Fundamental Theorem of Calculus and Accumulation Functions |
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269 | (2) |
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Interpreting the Behavior of Accumulation Functions Involving Area |
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271 | (4) |
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Applying Properties of Definite Integrals |
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275 | (1) |
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The Fundamental Theorem of Calculus and Definite Integrals |
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276 | (1) |
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Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation |
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277 | (9) |
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Integrating Using Substitution |
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286 | (14) |
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Advanced Integrals of Trig Functions |
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300 | (10) |
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Integrating Functions Using Long Division and Completing the Square |
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310 | (4) |
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Integration Using Integration by Parts |
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314 | (5) |
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Using Linear Partial Fractions |
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319 | (3) |
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Evaluating Improper Integrals |
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322 | (3) |
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Selecting Techniques for Antidifferentiation |
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325 | (3) |
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328 | (3) |
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331 | (26) |
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Modeling Situations with Differential Equations |
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332 | (1) |
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Verifying Solutions for Differential Equations |
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332 | (1) |
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333 | (4) |
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Reasoning Using Slope Fields |
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337 | (2) |
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Approximating Solutions Using Euler's Method |
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339 | (6) |
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Finding General Solutions Using Separation of Variables |
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345 | (1) |
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Finding Particular Solutions Using Initial Conditions and Separation of Variables |
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346 | (4) |
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Exponential Models with Differential Equations |
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350 | (2) |
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Logistic Models with Differential Equations |
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352 | (4) |
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356 | (1) |
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10 Applications Of Integration |
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357 | (30) |
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Finding the Average Value of a Function on an Interval |
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358 | (2) |
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Connecting Position, Velocity, and Acceleration Functions Using Integrals |
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360 | (1) |
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Using Accumulation Functions and Definite Integrals in Applied Contexts |
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361 | (1) |
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Finding the Area Between Curves Expressed as Functions of x |
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362 | (2) |
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Finding the Area Between Curves Expressed as Functions of y |
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364 | (3) |
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Finding the Area Between Curves That Intersect at More Than Two Points |
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367 | (1) |
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Volumes with Cross-Sections: Squares and Rectangles |
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368 | (2) |
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Volumes with Cross-Sections: Triangles and Semicircles |
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370 | (1) |
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Volume with Disc Method: Revolving Around the x- or Y-Axis |
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371 | (3) |
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Volume with Disc Method: Revolving Around Other Axes |
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374 | (1) |
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Volume with Washer Method: Revolving Around the x- or Y-Axis |
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375 | (3) |
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Volume with Washer Method: Revolving Around Other Axes |
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378 | (3) |
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The Arc Length of a Smooth, Planar Curve and Distance Traveled |
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381 | (3) |
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384 | (3) |
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11 Parametric Equations, Polar Coordinates, And Vector-Valued Functions |
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387 | (18) |
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Defining and Differentiating Parametric Equations |
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388 | (2) |
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Second Derivatives of Parametric Equations |
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390 | (1) |
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Finding Arc Lengths of Curves Given by Parametric Equations |
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391 | (2) |
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Defining and Differentiating Vector-Valued Functions |
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393 | (1) |
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Integrating Vector-Valued Functions |
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394 | (2) |
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Solving Motion Problems Using Parametric and Vector-Valued Functions |
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396 | (2) |
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Defining Polar Coordinates and Differentiating in Polar Form |
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398 | (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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399 | (2) |
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Finding the Area of the Region Bounded by Two Polar Curves |
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401 | (2) |
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403 | (2) |
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12 Infinite Sequences And Series |
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405 | (30) |
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Defining Convergent and Divergent Infinite Series |
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406 | (3) |
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Working with Geometric Series |
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409 | (2) |
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The nth Term Test for Divergence |
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411 | (1) |
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Integral Test for Convergence |
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412 | (1) |
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Harmonic Series and p-Series |
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413 | (2) |
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Comparison Tests for Convergence |
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415 | (3) |
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Alternating Series Test for Convergence |
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418 | (1) |
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Ratio Test for Convergence |
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419 | (1) |
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Determining Absolute or Conditional Convergence |
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420 | (1) |
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Alternating Series Error Bound |
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421 | (1) |
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Finding Taylor Polynomial Approximations of Functions |
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422 | (2) |
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424 | (1) |
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Radius and Interval of Convergence of Power Series |
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425 | (1) |
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Finding Taylor or Maclaurin Series for a Function |
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426 | (2) |
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Representing Functions as Power Series |
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428 | (5) |
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433 | (2) |
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13 Answers To Practice Problem Sets |
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435 | (158) |
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14 Answers To End Of
Chapter Drills |
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593 | (34) |
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627 | |
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629 | (30) |
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16 Practice Test 2: Answers And Explanations |
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659 | (32) |
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691 | (32) |
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18 Practice Test 3: Answers And Explanations |
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