1 Functions, Graphs, and Limits 1

1.1 The Cartesian Plane and the Distance Formula 2

1.2 Graphs of Equations 11

Project: Number of Stores 21

1.3 Lines in the Plane and Slope 22

Quiz Yourself 34

1.4 Functions 35

1.5 Limits 48

1.6 Continuity 60

Algebra Tutor 70

Summary and Study Strategies 72

Review Exercises 74

Test Yourself 78 

2 Differentiation 79

2.1 The Derivative and the Slope of a Graph 80

2.2 Some Rules for Differentiation 91

2.3 Rates of Change: Velocity and Marginals 103

2.4 The Product and Quotient Rules 117

Quiz Yourself 127

2.5 The Chain Rule 128

2.6 Higher-Order Derivatives 137

Project: Cell Phone Subscribers in U.S. 143

2.7 Implicit Differentiation 144

2.8 Related Rates 151

Algebra Tutor 158

Summary and Study Strategies 160

Review Exercises 162

Test Yourself 166 

3 Applications of the Derivative 167

3.1 Increasing and Decreasing Functions 168

3.2 Extrema and the First-Derivative Test 177

3.3 Concavity and the Second-Derivative Test 186

3.4 Optimization Problems 196

Quiz Yourself 204

3.5 Business and Economics Applications 205

3.6 Asymptotes 215

Project: Alternative-Fueled Vehicles 225

3.7 Curve Sketching: A Summary 226

3.8 Differentials and Marginal Analysis 235

Algebra Tutor 242

Summary and Study Strategies 244

Review Exercises 246

Test Yourself 250 

4 Exponential and Logarithmic Functions 251

4.1 Exponential Functions 252

4.2 Natural Exponential Functions 258

4.3 Derivatives of Exponential Functions 267

Quiz Yourself 275

4.4 Logarithmic Functions 276

4.5 Derivatives of Logarithmic Functions 285

4.6 Exponential Growth and Decay 294

Project: ATM Surcharge Fee 301

Algebra Tutor 302

Summary and Study Strategies 304

Review Exercises 306

Test Yourself 310 

5 Integration and Its Applications 311

5.1 Antiderivatives and Indefinite Integrals 312

5.2 Integration by Substitution and the General Power Rule 322

5.3 Exponential and Logarithmic Integrals 331

Quiz Yourself 338

5.4 Area and the Fundamental Theorem of Calculus 339

5.5 The Area of a Region Bounded by Two Graphs 351

Project: Social Security 359

5.6 The Definite Integral as the Limit of a Sum 360

Algebra Tutor 366

Summary and Study Strategies 368

Review Exercises 370

Test Yourself 374 

6 Techniques of Integration 375

6.1 Integration by Parts and Present Value 376

6.2 Integration Tables 386

Project: Purchasing Power of the Dollar 392

Quiz Yourself 393

6.3 Numerical Integration 394

6.4 Improper Integrals 403

Algebra Tutor 412

Summary and Study Strategies 414

Review Exercises 416

Test Yourself 418 

7 Functions of Several Variables 419

7.1 The Three-Dimensional Coordinate System 420

7.2 Surfaces in Space 427

7.3 Functions of Several Variables 436

7.4 Partial Derivatives 444

7.5 Extrema of Functions of Two Variables 455

Quiz Yourself 464

7.6 Lagrange Multipliers 465

7.7 Least Squares Regression Analysis 473

Project: Financial Data 479

7.8 Double Integrals and Area in the Plane 480

7.9 Applications of Double Integrals 488

Algebra Tutor 496

Summary and Study Strategies 498

Review Exercises 500

Test Yourself 504 

Appendices

Appendix A: Precalculus Review A2

A.1 The Real Number Line and Order A2

A.2 Absolute Value of a Real Number A8

A.3 Exponents and Radicals A13

A.4 Factoring Polynomials A19

A.5 Fractions and Rationalization A25

Appendix B: Alternate Introduction to the

Fundamental Theorem of Calculus A32

Appendix C: Formulas A41

C.1 Differentiation and Integration Formulas A41

C.2 Formulas from Business and Finance A45

Appendix D: Properties and Measurement (Web)*

D.1 Review of Algebra, Geometry, and Trigonometry

D.2 Units of Measurements

Appendix E: Graphing Utility Programs (Web)*

Appendix F: Differential Equations (Web)*

F.1 Solutions of Differential Equation

F.2 Separation of Variables

F.3 First-Order Linear Differential Equations

F.4 Applications of Differential Equations

Answers to Selected Exercises A47

Answers to Checkpoints A104

Answers to Tech Tutors A111

Index A112