Calculus and its applications: expanded version: media update

Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Contents......Page 5
Preface......Page 8
Prerequisite Skills Diagnostic Test......Page 22
Chapter R Functions, Graphs, and Models......Page 24
 R.1 Graphs and Equations......Page 25
 R.2 Functions and Models......Page 36
 R.3 Finding Domain and Range......Page 47
 R.4 Slope and Linear Functions......Page 56
 R.5 Nonlinear Functions and Models......Page 73
 R.6 Mathematical Modeling and Curve Fitting......Page 91
 Chapter Summary......Page 102
 Chapter Review Exercises......Page 108
 Chapter Test......Page 111
 Extended Technology Application: Average Price of a Movie Ticket......Page 113
Chapter 1 Differentiation......Page 116
 1.1 Limits: A Numerical and Graphical Approach......Page 117
 1.2 Algebraic Limits and Continuity......Page 132
 1.3 Average Rates of Change......Page 144
 1.4 Differentiation Using Limits of Difference Quotients......Page 155
 1.5 Differentiation Techniques: The Power and Sum–Difference Rules......Page 167
 1.6 Differentiation Techniques: The Product and Quotient Rules......Page 181
 1.7 The Chain Rule......Page 189
 1.8 Higher-Order Derivatives......Page 200
 Chapter Summary......Page 208
 Chapter Review Exercises......Page 213
 Chapter Test......Page 215
 Extended Technology Application: Path of a Baseball: The Tale of the Tape......Page 217
Chapter 2 Applications of Differentiation......Page 220
 2.1 Using First Derivatives to Find Maximum and Minimum Values and Sketch Graphs......Page 221
 2.2 Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs......Page 239
 2.3 Graph Sketching: Asymptotes and Rational Functions......Page 257
 2.4 Using Derivatives to Find Absolute Maximum and Minimum Values......Page 273
 2.5 Maximum–Minimum Problems; Business and Economics Applications......Page 285
 2.6 Marginals and Differentials......Page 300
 2.7 Implicit Differentiation and Related Rates......Page 311
 Chapter Summary......Page 318
 Chapter Review Exercises......Page 324
 Chapter Test......Page 326
 Extended Technology Application: Maximum Sustainable Harvest......Page 328
Chapter 3 Exponential and Logarithmic Functions......Page 330
 3.1 Exponential Functions......Page 331
 3.2 Logarithmic Functions......Page 345
 3.3 Applications: Uninhibited and Limited Growth Models......Page 360
 3.4 Applications: Decay......Page 376
 3.5 The Derivatives of ax and log ax......Page 389
 3.6 An Economics Application: Elasticity of Demand......Page 394
 Chapter Summary......Page 401
 Chapter Review Exercises......Page 405
 Chapter Test......Page 407
 Extended Technology Application: The Business of Motion Picture Revenue and DVD Release......Page 408
Chapter 4 Integration......Page 412
 4.1 Antidifferentiation......Page 413
 4.2 Antiderivatives as Areas......Page 422
 4.3 Area and Definite Integrals......Page 433
 4.4 Properties of Definite Integrals......Page 448
 4.5 Integration Techniques: Substitution......Page 459
 4.6 Integration Techniques: Integration by Parts......Page 468
 4.7 Integration Techniques: Tables......Page 477
 Chapter Summary......Page 482
 Chapter Review Exercises......Page 489
 Chapter Test......Page 491
 Extended Technology Application: Business: Distribution of Wealth......Page 492
Chapter 5 Applications of Integration......Page 496
 5.1 An Economics Application: Consumer Surplus and Producer Surplus......Page 497
 5.2 Applications of Integrating Growth and Decay Models......Page 503
 5.3 Improper Integrals......Page 515
 5.4 Numerical Integration......Page 521
 5.5 Volume......Page 533
 Chapter Summary......Page 538
 Chapter Review Exercises......Page 543
 Chapter Test......Page 545
 Extended Technology Application: Curve Fitting and Volumes of Containers......Page 546
Chapter 6 Functions of Several Variables......Page 548
 6.1 Functions of Several Variables......Page 549
 6.2 Partial Derivatives......Page 557
 6.3 Maximum–Minimum Problems......Page 566
 6.4 An Application: The Least-Squares Technique......Page 573
 6.5 Constrained Optimization......Page 580
 6.6 Double Integrals......Page 589
 Chapter Summary......Page 595
 Chapter Review Exercises......Page 599
 Chapter Test......Page 600
 Extended Technology Application: Minimizing Employees’ Travel Time in a Building......Page 601
Chapter 7 Trigonometric Functions......Page 604
 7.1 Basics of Trigonometry......Page 605
 7.2 Derivatives of Trigonometric Functions......Page 620
 7.3 Integration of Trigonometric Functions......Page 630
 7.4 Inverse Trigonometric Functions and Applications......Page 637
 Chapter Summary......Page 646
 Chapter Review Exercises......Page 649
 Chapter Test......Page 651
 Extended Technology Application: Parametric Curves......Page 653
Chapter 8 Differential Equations......Page 656
 8.1 Differential Equations......Page 657
 8.2 Separable Differential Equations......Page 663
 8.3 Applications: Inhibited Growth Models......Page 669
 8.4 First-Order Linear Differential Equations......Page 680
 8.5 Higher-Order Differential Equations and a Trigonometry Connection......Page 687
 Chapter Summary......Page 696
 Chapter Review Exercises......Page 699
 Chapter Test......Page 700
 Extended Technology Application: Visual (Slope Fields) and Numerical (Euler’s Method) Solutions of Differential Equations......Page 702
Chapter 9 Sequences and Series......Page 706
 9.1 Arithmetic Sequences and Series......Page 707
 9.2 Geometric Sequences and Series......Page 714
 9.3 Simple and Compound Interest......Page 724
 9.4 Annuities and Amortization......Page 732
 9.5 Power Series and Linearization......Page 743
 9.6 Taylor Series and a Trigonometry Connection......Page 751
 Chapter Summary......Page 759
 Chapter Review Exercises......Page 762
 Chapter Test......Page 764
 Extended Technology Application: Sequences and Series on a Spreadsheet......Page 765
Chapter 10 Probability Distributions......Page 770
 10.1 A Review of Sets......Page 771
 10.2 Probability......Page 779
 10.3 Discrete Probability Distributions......Page 790
 10.4 Continuous Probability Distributions......Page 801
 10.5 Mean, Variance, Standard Deviation, and the Normal Distribution......Page 812
 Chapter Summary......Page 826
 Chapter Review Exercises......Page 831
 Chapter Test......Page 832
 Extended Technology Application: Experimental Probability and the Law of Large Numbers......Page 834
Cumulative Review......Page 838
 Appendix A: Review of Basic Algebra......Page 842
 Appendix B: Indeterminate Forms and l’Hôpital’s Rule......Page 853
 Appendix C: Regression and Microsoft Excel......Page 859
 Appendix D: MathPrint Operating System for TI-84 and TI-84 Plus Silver Edition......Page 861
 Table A: Areas for a Standard Normal Distribution......Page 864
Photo Credits......Page 865
Chapter 11 Systems and Matrices......Page 866
 11.1 Systems of Linear Equations......Page 867
 11.2 Gauss-Jordan Elimination......Page 876
 11.3 Matrices and Row Operations......Page 883
 11.4 Matrix Arithmetic: Equality, Addition, and Scalar Multiples......Page 892
 11.5 Matrix Multiplication, Multiplicative Identities, and Inverses......Page 901
 11.6 Determinants and Cramer’s Rule......Page 913
 11.7 Systems of Linear Inequalities andLinear Programming......Page 923
Chapter 12 Discrete Probability......Page 948
 12.1 Compound Events and Odds......Page 949
 12.2 Combinatorics: The Multiplication Principal and the Factorial......Page 962
 12.3 Permutations and Combinations......Page 970
 12.4 Conditional Probability and the Hypergeometric Distribution Model......Page 979
 12.5 Independence, Bernoulli Trials and the Binomial Probability Model......Page 992
 12.6 Bayes Rule......Page 1007
Answers......Page 1043
Index of Applications......Page 1098
Index......Page 1102