Calculus for business, economics, and the social and life sciences

Cover Page......Page 1
Half Title Page1......Page 2
Title Page......Page 4
Copyright Page......Page 5
Dedication......Page 6
Contents......Page 8
Preface......Page 12
Key Features of This Text......Page 15
Acknowledgments......Page 21
Half Title Page2......Page 24
CHAPTER1 Functions, Graphs, and Limits......Page 26
1.1 Functions......Page 27
1.2 The Graph of a Function......Page 41
1.3 Lines and Linear Functions......Page 55
1.4 Functional Models......Page 70
1.5 Limits......Page 88
1.6 One-Sided Limits and Continuity......Page 103
Checkup for Chapter 1......Page 116
Review Exercises......Page 117
Explore! Update......Page 122
Think About It......Page 124
CHAPTER 2 Differentiation: Basic Concepts......Page 128
2.1 The Derivative......Page 129
2.2 Techniques of Differentiation......Page 144
2.3 Product and Quotient Rules; Higher-Order Derivatives......Page 157
2.4 The Chain Rule......Page 171
2.5 Marginal Analysis and Approximations Using Increments......Page 185
2.6 Implicit Differentiation and Related Rates......Page 197
Important Terms, Symbols, and Formulas......Page 210
Review Exercises......Page 211
Explore! Update......Page 218
Think About It......Page 220
CHAPTER 3 Additional Applications of the Derivative......Page 222
3.1 Increasing and Decreasing Functions; Relative Extrema......Page 223
3.2 Concavity and Points of Inflection......Page 240
3.3 Curve Sketching......Page 258
3.4 Optimization; Elasticity of Demand......Page 273
3.5 Additional Applied Optimization......Page 291
Checkup for Chapter 3......Page 310
Review Exercises......Page 312
Explore! Update......Page 317
Think About It......Page 319
CHAPTER 4 Exponential and Logarithmic Functions......Page 322
4.1 Exponential Functions; Continuous Compounding......Page 323
4.2 Logarithmic Functions......Page 339
4.3 Differentiation of Exponential and Logarithmic Functions......Page 355
4.4 Additional Applications; Exponential Models......Page 370
Important Terms, Symbols, and Formulas......Page 387
Checkup for Chapter 4......Page 388
Review Exercises......Page 389
Explore! Update......Page 395
Think About It......Page 397
CHAPTER 5 Integration......Page 400
5.1 Indefinite Integration and Differential Equations......Page 401
5.2 Integration by Substitution......Page 417
5.3 The Definite Integral and the Fundamental Theorem of Calculus......Page 432
5.4 Applying Definite Integration: Distribution of Wealth and Average Value......Page 448
5.5 Additional Applications of Integration to Business and Economics......Page 467
5.6 Additional Applications of Integration to the Life and Social Sciences......Page 478
Important Terms, Symbols, and Formulas......Page 492
Checkup for Chapter 5......Page 493
Review Exercises......Page 494
Explore! Update......Page 499
Think About It......Page 502
CHAPTER 6 Additional Topics in Integration......Page 504
6.1 Integration by Parts; Integral Tables......Page 505
6.2 Numerical Integration......Page 519
6.3 Improper Integrals......Page 533
6.4 Introduction to Continuous Probability......Page 542
Important Terms, Symbols, and Formulas......Page 555
Checkup for Chapter 6......Page 556
Review Exercises......Page 557
Explore! Update......Page 560
Think About It......Page 563
CHAPTER 7 Calculus of Several Variables......Page 570
7.1 Functions of Several Variables......Page 571
7.2 Partial Derivatives......Page 586
7.3 Optimizing Functions of Two Variables......Page 602
7.4 The Method of Least-Squares......Page 619
7.5 Constrained Optimization: The Method of Lagrange Multipliers......Page 631
7.6 Double Integrals......Page 646
Important Terms, Symbols, and Formulas......Page 663
Checkup for Chapter 7......Page 664
Review Exercises......Page 665
Explore! Update......Page 670
Think About It......Page 672
APPENDIX A Algebra Review......Page 676
A.1 A Brief Review of Algebra......Page 677
A.2 Factoring Polynomials and Solving Systems of Equations......Page 688
A.3 Evaluating Limits with L’Hôpital’s Rule......Page 700
A.4 The Summation Notation......Page 705
Important Terms, Symbols, and Formulas......Page 706
Review Exercises......Page 707
Think About It......Page 709
TABLES I Powers of e......Page 710
II The Natural Logarithm (Base e)......Page 711
TEXT SOLUTIONS Answers to Odd-Numbered Exercises, Checkup Exercises, and Review Exercises......Page 712
Index......Page 796
Index of Applications......Page 802