Calculus for Business Economics & the Social & Life Sciences, Brief 10th Edition

Cover Page......Page 1
Calculus:
For Business, Economics, and the Social and Life Sciences......Page 4
ISBN 9780073532318......Page 5
Preface......Page 9
CONTENTS......Page 6
CHAPTER 1: Functions, Graphs, and Limits......Page 18
1.1 Functions......Page 19
1.2 The Graph of a Function......Page 32
1.3 Linear Functions......Page 46
1.4 Functional Models......Page 62
1.5 Limits......Page 80
1.6 One-Sided Limits and Continuity......Page 95
Checkup for Chapter 1......Page 107
Review Exercises......Page 108
Explore! Update......Page 113
Think About It......Page 115
CHAPTER 2: Differentiation: Basic Concepts......Page 118
2.1 The Derivative......Page 119
2.2 Techniques of Differentiation......Page 134
2.3 Product and Quotient Rules; Higher-Order Derivatives......Page 146
2.4 The Chain Rule......Page 159
2.5 Marginal Analysis and Approximations Using Increments......Page 173
2.6 Implicit Differentiation and Related Rates......Page 184
Important Terms, Symbols, and Formulas......Page 196
Checkup for Chapter 2......Page 197
Review Exercises......Page 198
Explore! Update......Page 204
Think About It......Page 206
CHAPTER 3: Additional Applications of the Derivative......Page 208
3.1 Increasing and Decreasing Functions; Relative Extrema......Page 209
3.2 Concavity and Points of Inflection......Page 225
3.3 Curve Sketching......Page 242
3.4 Optimization; Elasticity of Demand......Page 257
3.5 Additional Applied Optimization......Page 276
Important Terms, Symbols, and Formulas......Page 294
Checkup for Chapter 3......Page 295
Review Exercises......Page 296
Explore! Update......Page 302
Think About It......Page 304
CHAPTER 4: Exponential and Logarithmic Functions......Page 308
4.1 Exponential Functions; Continuous Compounding......Page 309
4.2 Logarithmic Functions......Page 325
4.3 Differentiation of Exponential and Logarithmic Functions......Page 342
4.4 Applications; Exponential Models......Page 357
Important Terms, Symbols, and Formulas......Page 374
Checkup for Chapter 4......Page 375
Review Exercises......Page 376
Explore! Update......Page 382
Think About It......Page 384
CHAPTER 5: Integration......Page 388
5.1 Antidifferentiation: The Indefinite Integral......Page 389
5.2 Integration by Substitution......Page 402
5.3 The Definite Integral and the Fundamental Theorem of Calculus......Page 414
5.4 Applying Definite Integration: Area Between Curves and Average Value......Page 431
5.5 Additional Applications to Business and Economics......Page 449
5.6 Additional Applications to the Life and Social Sciences......Page 462
Important Terms, Symbols, and Formulas......Page 479
Checkup for Chapter 5......Page 480
Review Exercises......Page 481
Explore! Update......Page 486
Think About It......Page 489
CHAPTER 6: Additional Topics in Integration......Page 492
6.1 Integration by Parts; Integral Tables......Page 493
6.2 Introduction to Differential Equations......Page 507
6.3 Improper Integrals; Continuous Probability......Page 526
6.4 Numerical Integration......Page 543
Important Terms, Symbols, and Formulas......Page 557
Checkup for Chapter 6......Page 558
Review Exercises......Page 559
Explore! Update......Page 565
Think About It......Page 568
CHAPTER 7: Calculus of Several Variables......Page 574
7.1 Functions of Several Variables......Page 575
7.2 Partial Derivatives......Page 590
7.3 Optimizing Functions of Two Variables......Page 605
7.4 The Method of Least-Squares......Page 618
7.5 Constrained Optimization: The Method of Lagrange Multipliers......Page 630
7.6 Double Integrals......Page 641
Important Terms, Symbols, and Formulas......Page 661
Checkup for Chapter 7......Page 662
Review Exercises......Page 663
Explore! Update......Page 668
Think About It......Page 670
APPENDIX A: Algebra Review......Page 674
A.1 A Brief Review of Algebra......Page 675
A.2 Factoring Polynomials and Solving Systems of Equations......Page 686
A.3 Evaluating Limits with L'Hôpital's Rule......Page 699
A.4 The Summation Notation......Page 704
Important Terms, Symbols, and Formulas......Page 705
Review Exercises......Page 706
TABLES......Page 709
I Powers of e......Page 710
II The Natural Logarithm (Base e)......Page 711
Answers to Odd-Numbered Excercises, Chapter Checkup Exercises, and Odd-Numbered Chapter Review Exercises......Page 712
Index......Page 796