Includes index.

Contents
Preface vi
c h a p t e r 1 functions, graphs, and limits
1 functions 2
2 the graph of a function 14
3 linear functions 26
4 functional models 41
5 limits 57
6 one-sided limits and continuity 71
Chapter summary 83
Important terms, symbols, and formulas 83
Checkup for chapter 1 83
Review problems 84
Explore! Update 89
Think about it 91
C h a p t e r 2 differentiation: basic concepts
1 the derivative 96
2 techniques of differentiation 110
3 product and quotient rules; higher-order derivatives 122
4 the chain rule 135
5 marginal analysis and approximations using increments 147
6 implicit differentiation and related rates 158
Chapter summary 170
Important terms, symbols, and formulas 170
Checkup for chapter 2 171
Review problems 172
Explore! Update 178
Think about it 180
C h a p t e r 3 additional applications of the derivative
1 increasing and decreasing functions; relative extrema 184
2 concavity and points of inflection 199
3 curve sketching 216
4 optimization 231
5 additional applied optimization 249
Chapter summary 266
Important terms, symbols, and formulas 266
Checkup for chapter 3 267
Review problems 268
Explore! Update 274
Think about it 277
C h a p t e r 4 exponential and logarithmic functions
1 exponential functions 282
2 logarithmic functions 297
3 differentiation of logarithmic and exponential functions 312
4 additional exponential models 326
Chapter summary 340
Important terms, symbols, and formulas 340
Checkup for chapter 4 342
Review problems 343
Explore! Update 349
Think about it 351
C h a p t e r 5 integration
1 antidifferentiation: the indefinite integral 356
2 integration by substitution 368
3 the definite integral and the fundamental theorem of calculus 380
4 applying definite integration: area between curves and average value 396
5 additional applications to business and economics 414
6 additional applications to the life and social sciences 426
Chapter summary 436
Important terms, symbols, and formulas 436
Checkup for chapter 5 437
Review problems 438
Explore! Update 442
Think about it 445
C h a p t e r 6 additional topics in integration
1 integration by parts; integral tables 450
2 introduction to differential equations 464
3 improper integrals; continuous probability 480
4 numerical integration 496
Chapter summary 508
Important terms, symbols, and formulas 508
Checkup for chapter 6 509
Review problems 510
Explore! Update 516
Think about it 519
C h a p t e r 7 calculus of several variables
1 functions of several variables 526
2 partial derivatives 540
3 optimizing functions of two variables 551
4 the method of least-squares 563
5 constrained optimization: the method of lagrange multipliers 575
6 double integrals over rectangular regions 589