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사이즈 비교   소득공제 외서

## AP Calculus Premium, 2024: 12 Practice Tests + Comprehensive Review + Online Practice

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| | 2023년 07월 04일   저자/출판사 더보기/감추기
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발행일 2023년 07월 04일 672쪽 | 211*274*35mm 9781506287836 1506287832

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 How to Use This Book ix Barron's Essential 5 x Introduction 1 The Courses 1 Topic Outline for the AB and BC Calculus Exams 1 The Examinations 7 The Graphing Calculator: Using Your Graphing Calculator on the AP Exam 8 Grading the Examinations 12 Diagnostic Tests Diagnostic Test Calculus AB 17 Diagnostic Test Calculus BC 41 Topical Review and Practice 1. Functions 63 A Definitions 63 B Special Functions 66 C Polynomial and Other Rational Functions 69 D Trigonometric Functions 69 E Exponential and Logarithmic Functions 72 F Parametrically Defined Functions 73 G Polar Functions 76 Practice Exercises 79 2. Limits and Continuity 89 A Definitions and Examples 89 B Asymptotes 94 C Theorems on Limits 96 D Limit of a Quotient of Polynomials 98 E Other Basic Limits 99 F Continuity 99 Practice Exercises 105 3. Differentiation 113 A Definition of Derivative 113 B Formulas 115 C The Chain Rule: The Derivative of a Composite Function 116 D Differentiability and Continuity 121 E Estimating a Derivative 122 E1 Numerically 122 E2 Graphically 125 F Derivatives of Parametrically Defined Functions 126 G Implicit Differentiation 128 H Derivative of the Inverse of a Function 130 I The Mean Value Theorem 131 J Indeterminate Forms and L'Hospital's Rule 133 K Recognizing a Given Limit as a Derivative 136 Practice Exercises 139 4. Applications of Differential Calculus 159 A Slope; Critical Points 159 B Tangents to a Curve 161 C Increasing and Decreasing Functions 163 Case I Functions with Continuous Derivatives 163 Case II Functions Whose Derivatives Have Discontinuities 163 D Maximum, Minimum, Concavity, and Inflection Points: Definitions 164 E Maximum, Minimum, and Inflection Points: Curve Sketching 165 Case I Functions That Are Everywhere Differentiable 165 Case II Functions Whose Derivatives May Not Exist Everywhere 169 F Global Maximum or Minimum 171 Case I Differentiable Functions 171 Case II Functions That Are Not Everywhere Differentiable 171 G Further Aids in Sketching 171 H Optimization: Problems Involving Maxima and Minima 173 I Relating a Function and Its Derivatives Graphically 177 J Motion Along a Line 180 K Motion Along a Curve: Velocity and Acceleration Vectors 182 L Tangent-Line Approximations 186 M Related Rates 188 N Slope of a Polar Curve 190 Practice Exercises 193 5. Antidifferentiation 213 A Antiderivatives 213 B Basic Formulas 213 C Integration by Partial Fractions 220 D Integration by Parts 221 E Applications of Antiderivatives; Differential Equations 224 Practice Exercises 227 6. Definite Integrals 241 A Fundamental Theorem of Calculus (FTC); Evaluation of Definite integrals 241 B Properties of Definite Integrals 241 C Definition of Definite integral as the Limit of a Riemann Sum 246 D The Fundamental Theorem Again 247 E Approximations of the Definite Integral; Riemann Sums 248 E1 Using Rectangles 248 E2 Using Trapezoids 250 E3 Comparing Approximating Sums 252 F Graphing a Function from Its Derivative; Another Look 253 G Interpreting In x as an Area 260 H Average Value 261 Practice Exercises 270 7. Applications of Integration to Geometry 283 A Area 283 A1 Area Between Curves 285 A2 Using Symmetry 286 A3 Region Bounded by Polar Curve 288 B Volume 290 B1 Solids with Known Cross Sections 290 B2 Solids of Revolution 292 C Length of Curve (Arc Length) 297 D Improper Integrals 299 Practice Exercises 309 8. Further Applications of Integration 337 A Motion Along a Straight Line 337 B Motion Along a Plane Curve 339 C Other Applications of Riemann Sums 342 D FTC: Definite Integral of a Rate Is Net Change 344 Practice Exercises 346 9. Differential Equations 357 A Basic Definitions 357 B Slope Fields 358 C Euler's Method 363 D Solving First-Order Differential Equations Analytically 367 E Exponential Growth and Decay 369 Case I Exponential Growth 369 Case II Restricted Growth 373 Case III Logistic Growth 376 Practice Exercises 381 10. Sequences and Series 399 A Sequences of Real Numbers 399 B Infinite Series 400 B1 Definitions 400 B2 Theorems About Convergence or Divergence of Infinite Series 402 B3 Tests for Convergence of Infinite Series 403 B4 Tests for Convergence of Nonnegative Series 404 B5 Alternating Series and Absolute Convergence 408 C Power Series 411 C1 Definitions; Convergence 411 C2 Functions Defined by Power Series 413 C3 Finding a Power Series for a Function: Taylor and Maclaurin Series 415 C4 Approximating Functions with Taylor and Maclaurin Polynomials 418 C5 Taylor's Formula with Remainder; Lagrange Error Bound 423 C6 Computations with Power Series 425 C7 Power Series over Complex Numbers 429 Practice Exercises 431 11. Miscellaneous Multiple-Choice Practice Questions 443 12. Miscellaneous Free-Response Practice Exercises 475 AB Practice Tests AB Practice Test 1 505 AB Practice Test 2 529 AB Practice Test 3 555 BC Practice Tests BC Practice Test 1 583 BC Practice Test 2 605 BC Practice Test 3 625 Appendix: Formulas and Theorems for Reference 645 Index 653
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