Calculus and its applications [11th edition] 9780321979391, 1292100249, 9781292100241, 0321979397

Table of contents :
Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Contents......Page 5
Preface......Page 7
Prerequisite Skills Diagnostic Test......Page 16
Functions, Graphs, and Models......Page 18
R.1 Graphs and Equations......Page 19
R.2 Functions and Models......Page 30
R.3 Finding Domain and Range......Page 42
R.4 Slope and Linear Functions......Page 51
R.5 Nonlinear Functions and Models......Page 65
R.6 Mathematical Modeling and Curve Fitting......Page 84
Chapter Summary......Page 96
Chapter Review Exercises......Page 102
Chapter Test......Page 105
Extended Technology Application Average Price of a Movie Ticket......Page 107
Differentiation......Page 109
1.1 Limits: A Numerical and Graphical Approach......Page 110
1.2 Algebraic Limits and Continuity......Page 123
1.3 Average Rates of Change......Page 133
1.4 Differentiation Using Limits of Difference Quotients......Page 144
1.5 Differentiation Techniques: The Power and Sum–Difference Rules......Page 155
1.6 Differentiation Techniques: The Product and Quotient Rules......Page 166
1.7 The Chain Rule......Page 174
1.8 Higher-Order Derivatives......Page 184
Chapter Summary......Page 193
Chapter Review Exercises......Page 198
Chapter Test......Page 200
Extended Technology Application Path of a Baseball: The Tale of the Tape......Page 202
Applications of Differentiation......Page 205
2.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs......Page 206
2.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs......Page 221
2.3 Graph Sketching: Asymptotes and Rational Functions......Page 237
2.4 Using Derivatives to Find Absolute Maximum and Minimum Values......Page 250
2.5 Maximum–Minimum Problems; Business, Economics, and General Applications......Page 261
2.6 Marginals and Differentials......Page 276
2.7 Elasticity of Demand......Page 286
2.8 Implicit Differentiation and Related Rates*......Page 291
Chapter Summary......Page 299
Chapter Review Exercises......Page 305
Chapter Test......Page 307
Extended Technology Application Maximum Sustainable Harvest......Page 309
Exponential and Logarithmic Functions......Page 311
3.1 Exponential Functions......Page 312
3.2 Logarithmic Functions......Page 324
3.3 Applications: Uninhibited and Limited Growth Models......Page 339
3.4 Applications: Decay......Page 354
3.5 The Derivatives of ax and log ax; Application: Annuities......Page 366
3.6 A Business Application: Amortization*......Page 372
Chapter Summary......Page 379
Chapter Review Exercises......Page 383
Chapter Test......Page 385
Extended Technology Application The Business of Motion Picture Revenue and DVD Release......Page 387
Integration......Page 389
4.1 Antidifferentiation......Page 390
4.2 Antiderivatives as Areas......Page 398
4.3 Area and Definite Integrals......Page 408
4.4 Properties of Definite Integrals......Page 422
4.5 Integration Techniques: Substitution......Page 433
4.6 Integration Techniques: Integration by Parts......Page 441
4.7 Integration Techniques: Tables......Page 448
Chapter Summary......Page 454
Chapter Review Exercises......Page 460
Chapter Test......Page 461
Extended technology Application Business: Distribution of Wealth......Page 463
Applications of Integration......Page 466
5.1 Consumer Surplus and Producer Surplus......Page 467
5.2 Integrating Growth and Decay Models......Page 473
5.3 Improper Integrals......Page 484
5.4 Probability......Page 490
5.5 Probability: Expected Value; The Normal Distribution......Page 500
5.6 Volume......Page 512
5.7 Differential Equations......Page 519
Chapter Summary......Page 530
Chapter Review Exercises......Page 536
Chapter Test......Page 538
Extended Technology Application Curve Fitting and Volumes of Containers......Page 540
Functions of Several Variables......Page 542
6.1 Functions of Several Variables......Page 543
6.2 Partial Derivatives......Page 551
6.3 Maximum–Minimum Problems......Page 559
6.4 An Application: The Least-Squares Technique......Page 565
6.5 Constrained Optimization......Page 573
6.6 Double Integrals......Page 584
Chapter Summary......Page 590
Chapter Review Exercises......Page 594
Chapter Test......Page 595
Extended Technology Application Minimizing Employees’ Travel Time in a Building......Page 596
Cumulative Review......Page 598
Appendix A: Review of Basic Algebra......Page 602
Appendix B: Regression and Microsoft Excel......Page 616
Table A: Areas for a Standard Normal Distribution......Page 620
Answers......Page 622
Index of Applications......Page 662
Index......Page 666