AP微积分BC5分制胜 英文 第2版【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

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STEP 1 Set Up Your Study Plan3

1 What You Need to Know About the AP Calculus BC Exam3

1.1 What Is Covered on the AP Calculus BC Exam？4

1.2 What Is the Format of the AP Calculus BC Exam？4

1.3 What Are the Advanced Placement Exam Grades？5

How Is the AP Calculus BC Exam Grade Calculated？5

1.4 Which Graphing Calculators Are Allowed for the Exam？6

Calculators and Other Devices Not Allowed for the AP Calculus BC Exam7

Other Restrictions on Calculators7

2 How to Plan Your Time8

2.1 Three Approaches to Preparing for the AP Calculus BC Exam8

Overview of the Three Plans8

2.2 Calendar for Each Plan10

Summary of the Three Study Plans13

STEP 2 Determine Your Test Readiness17

3 Take a Diagnostic Exam17

3.1 Getting Started！21

3.2 Diagnostic Test21

3.3 Answers to Diagnostic Test27

3.4 Solutions to Diagnostic Test28

3.5 Calculate Your Score38

Short-Answer Questions38

AP Calculus BC Diagnostic Exam38

STEP 3 Develop Strategies for Success41

4 How to Approach Each Question Type41

4.1 The Multiple-Choice Questions42

4.2 The Free-Response Questions42

4.3 Using a Graphing Calculator43

4.4 Taking the Exam44

What Do I Need to Bring to the Exam？44

Tips for Taking the Exam45

STEP 4 Review the Knowledge You Need to Score High49

5 Limits and Continuity49

5.1 The Limit of a Function50

Definition and Properties of Limits50

Evaluating Limits50

One-Sided Limits52

Squeeze Theorem55

5.2 Limits Involving Infinities57

Infinite Limits（as x→a）57

Limits at Infinity（as x→±∞）59

Horizontal and Vertical Asymptotes61

5.3 Continuity of a Function64

Continuity of a Function at a Number64

Continuity of a Function over an Interval64

Theorems on Continuity64

5.4 Rapid Review67

5.5 Practice Problems69

5.6 Cumulative Review Problems70

5.7 Solutions to Practice Problems70

5.8 Solutions to Cumulative Review Problems73

6 Differentiation75

6.1 Derivatives of Algebraic Functions76

Definition of the Derivative of a Function76

Power Rule79

The Sum,Difference,Product,and Quotient Rules80

The Chain Rule81

6.2 Derivatives of Trigonometric,Inverse Trigonometric,Exponential,and Logarithmic Functions82

Derivatives of Trigonometric Functions82

Derivatives of Inverse Trigonometric Functions84

Derivatives of Exponential and Logarithmic Functions85

6.3 Implicit Differentiation87

Procedure for Implicit Differentiation87

6.4 Approximating a Derivative90

6.5 Derivatives of Inverse Functions92

6.6 Higher Order Derivatives94

6.7 Indeterminate Forms95

L'H？pital's Rule for Indeterminate Forms95

6.8 Rapid Review95

6.9 Practice Problems97

6.10 Cumulative Review Problems98

6.11 Solutions to Practice Problems98

6.12 Solutions to Cumulative Review Problems101

7 Graphs of Functions and Derivatives103

7.1 Rolle's Theorem,Mean Value Theorem,and Extreme Value Theorem103

Rolle's Theorem104

Mean Value Theorem104

Extreme Value Theorem107

7.2 Determining the Behavior of Functions108

Test for Increasing and Decreasing Functions108

First Derivative Test and Second Derivative Test for Relative Extrema111

Test for Concavity and Points of Inflection114

7.3 Sketching the Graphs of Functions120

Graphing without Calculators120

Graphing with Calculators121

7.4 Graphs of Derivatives123

7.5 Parametric,Polar,and Vector Representations128

Parametric Curves128

Polar Equations129

Types of Polar Graphs129

Symmetry of Polar Graphs130

Vectors131

Vector Arithmetic132

7.6 Rapid Review133

7.7 Practice Problems137

7.8 Cumulative Review Problems139

7.9 Solutions to Practice Problems140

7.10 Solutions to Cumulative Review Problems147

8 Applications of Derivatives149

8.1 Related Rate149

General Procedure for Solving Related Rate Problems149

Common Related Rate Problems150

Inverted Cone（Water Tank）Problem151

Shadow Problem152

Angle of Elevation Problem153

8.2 Applied Maximum and Minimum Problems155

General Procedure for Solving Applied Maximum and Minimum Problems155

Distance Problem155

Area and Volume Problem156

Business Problems159

8.3 Rapid Review160

8.4 Practice Problems161

8.5 Cumulative Review Problems163

8.6 Solutions to Practice Problems164

8.7 Solutions to Cumulative Review Problems171

9 More Applications of Derivatives174

9.1 Tangent and Normal Lines174

Tangent Lines174

Normal Lines180

9.2 Linear Approximations183

Tangent Line Approximation（or Linear Approximation）183

Estimating the nth Root of a Number185

Estimating the Value of a Trigonometric Function of an Angle185

9.3 Motion Along a Line186

Instantaneous Velocity and Acceleration186

Vertical Motion188

Horizontal Motion188

9.4 Parametric,Polar,and Vector Derivatives190

Derivatives of Parametric Equations190

Position,Speed,and Acceleration191

Derivatives of Polar Equations191

Velocity and Acceleration of Vector Functions192

9.5 Rapid Review195

9.6 Practice Problems196

9.7 Cumulative Review Problems198

9.8 Solutions to Practice Problems199

9.9 Solutions to Cumulative Review Problems204

10 Integration207

10.1 Evaluating Basic Integrals208

Antiderivatives and Integration Formulas208

Evaluating Integrals210

10.2 Integration by U-Substitution213

The U-Substitution Method213

U-Substitution and Algebraic Functions213

U-Substitution and Trigonometric Functions215

U-Substitution and Inverse Trigonometric Functions216

U-Substitution and Logarithmic and Exponential Functions218

10.3 Techniques of Integration221

Integration by Parts221

Integration by Partial Fractions222

10.4 Rapid Review223

10.5 Practice Problems224

10.6 Cumulative Review Problems225

10.7 Solutions to Practice Problems226

10.8 Solutions to Cumulative Review Problems229

11 Definite Integrals231

11.1 Riemann Sums and Definite Integrals232

Sigma Notation or Summation Notation232

Definition of a Riemann Sum233

Definition of a Definite Integral234

Properties of Definite Integrals235

11.2 Fundamental Theorems of Calculus237

First Fundamental Theorem of Calculus237

Second Fundamental Theorem of Calculus238

11.3 Evaluating Definite Integrals241

Definite Integrals Involving Algebraic Functions241

Definite Integrals Involving Absolute Value242

Definite Integrals Involving Trigonometric,Logarithmic,and Exponential Functions243

Definite Integrals Involving Odd and Even Functions245

11.4 Improper Integrals246

Infinite Intervals of Integration246

Infinite Discontinuities247

11.5 Rapid Review248

11.6 Practice Problems249

11.7 Cumulative Review Problems250

11.8 Solutions to Practice Problems251

11.9 Solutions to Cumulative Review Problems254

12 Areas and Volumes257

12.1 The Function F（x）=？f（t）dt258

12.2 Approximating the Area Under a Curve262

Rectangular Approximations262

Trapezoidal Approximations266

12.3 Area and Definite Integrals267

Area Under a Curve267

Area Between Two Curves272

12.4 Volumes and Definite Integrals276

Solids with Known Cross Sections276

The Disc Method280

The Washer Method285

12.5 Integration of Parametric,Polar,and Vector Curves289

Area,Arc Length,and Surface Area for Parametric Curves289

Area and Arc Length for Polar Curves290

Integration of a Vector-Valued Function291

12.6 Rapid Review292

12.7 Practice Problems295

12.8 Cumulative Review Problems296

12.9 Solutions to Practice Problems297

12.10 Solutions to Cumulative Review Problems305

13 More Applications of Definite Integrals309

13.1 Average Value of a Function310

Mean Value Theorem for Integrals310

Average Value of a Function on［a,b］311

13.2 Distance Traveled Problems313

13.3 Definite Integral as Accumulated Change316

Business Problems316

Temperature Problem317

Leakage Problems318

Growth Problem318

13.4 Differential Equations319

Exponential Growth/Decay Problems319

Separable Differential Equations321

13.5 Slope Fields324

13.6 Logistic Differential Equations328

13.7 Euler's Method330

Approximating Solutions of Differential Equations by Euler's Method330

13.8 Rapid Review332

13.9 Practice Problems334

13.10 Cumulative Review Problems336

13.11 Solutions to Practice Problems337

13.12 Solutions to Cumulative Review Problems343

14 Series346

14.1 Sequences and Series347

Convergence347

14.2 Types of Series348

p-Series348

Harmonic Series348

Geometric Series348

Decimal Expansion349

14.3 Convergence Tests350

Integral Test350

Ratio Test351

Comparison Test351

Limit Comparison Test352

14.4 Alternating Series353

Error Bound354

Absolute Convergence354

14.5 Power Series354

Radius and Interval of Convergence355

14.6 Taylor Series355

Taylor Series and MacLaurin Series355

Common MacLaurin Series357

14.7 Operations on Series357

Substitution357

Differentiation and Integration358

Error Bounds359

14.8 Rapid Review360

14.9 Practice Problems362

14.10 Cumulative Review Problems363

14.11 Solutions to Practice Problems363

14.12 Solutions to Cumulative Review Problems366

STEP 5 Build Your Test-Taking Confidence371

AP Calculus BC Practice Exam 1371

AP Calculus BC Practice Exam 2401

AP Calculus BC Practice Exam 3433

Formulas and Theorems463

Bibliography and Websites471