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

Cover......Page 1
Contents......Page 4
Preface......Page 7
Diagnostic Prerequisite Test......Page 17
Part 1: A Library of Elementary Functions ......Page 20
 Chapter 1: Functions and Graphs......Page 21
   Graphs of Equations......Page 22
   Definition of a Function......Page 24
   Functions Specified by Equations......Page 25
   Function Notation......Page 28
   Applications......Page 30
   Exercises 1.1......Page 33
   A Beginning Library of Elementary Functions......Page 37
   Vertical and Horizontal Shifts......Page 39
   Reflections, Stretches, and Shrinks......Page 41
   Piecewise-Defined Functions......Page 43
   Exercises 1.2......Page 45
   Linear Functions, Equations, and Inequalities......Page 49
   Quadratic Functions, Equations, and Inequalities......Page 53
   Properties of Quadratic Functions and Their Graphs......Page 55
   Linear and Quadratic Regression......Page 62
   Exercises 1.3......Page 64
   Polynomial Functions......Page 71
   Regression Polynomials......Page 72
   Exercises 1.4......Page 78
   Exponential Functions......Page 81
   Base e Exponential Functions......Page 84
   Growth and Decay Applications......Page 85
   Compound Interest......Page 87
   Exercises 1.5......Page 89
  1.6 Logarithmic Functions......Page 92
   Logarithmic Functions......Page 93
   Calculator Evaluation of Logarithms......Page 97
   Exercises 1.6......Page 101
  Chapter 1: Summary and Review......Page 103
  Review Exercises......Page 106
Part 2: Calculus......Page 112
 Chapter 2: Limits and the Derivative......Page 113
   Functions and Graphs: Brief Review......Page 114
   Limits: A Graphical Approach......Page 115
   Limits: An Algebraic Approach......Page 119
   Limits of Difference Quotients......Page 123
   Exercises 2.1......Page 124
   Infinite Limits......Page 128
   Locating Vertical Asymptotes......Page 129
   Finding Horizontal Asymptotes......Page 134
   Exercises 2.2......Page 136
   Continuity......Page 140
   Continuity Properties......Page 144
   Solving Inequalities Using Continuity Properties......Page 145
   Exercises 2.3......Page 147
   Rate of Change......Page 151
   Slope of the Tangent Line......Page 154
   Exercises 2.4......Page 162
  2.5 Basic Differentiation Properties......Page 166
   Constant Multiple Property......Page 169
   Sum and Difference Properties......Page 170
   Exercises 2.5......Page 172
  2.6 Differentials......Page 175
   Exercises 2.6......Page 180
   Marginal Cost, Revenue, and Profit......Page 182
   Marginal Average Cost, Revenue, and Profit......Page 187
   Exercises 2.7......Page 189
  Chapter 2: Summary and Review......Page 193
  Review Exercises......Page 194
 Chapter 3: Additional Derivative Topics......Page 199
   Continuous Compound Interest......Page 200
   Exercises 3.1......Page 204
  3.2 Derivatives of Exponential and Logarithmic Functions......Page 206
   The Derivative of ln x......Page 207
   Other Logarithmic and Exponential Functions......Page 209
   Exponential and Logarithmic Models......Page 211
   Exercises 3.2......Page 213
   Derivatives of Products......Page 215
   Exercises 3.3......Page 220
   Composite Functions......Page 223
   General Power Rule......Page 224
   The Chain Rule......Page 227
   Exercises 3.4......Page 230
   Implicit Differentiation......Page 233
   Exercises 3.5......Page 237
  3.6 Related Rates......Page 239
   Exercises 3.6......Page 243
   Relative Rate of Change......Page 245
   Elasticity of Demand......Page 246
   Exercises 3.7......Page 250
  Chapter 3: Summary and Review......Page 252
  Review Exercises......Page 254
 Chapter 4: Graphing and Optimization......Page 256
   Increasing and Decreasing Functions......Page 257
   First-Derivative Test......Page 263
   Economics Applications......Page 265
   Exercises 4.1......Page 268
   Using Concavity as a Graphing Tool......Page 273
   Finding Inflection Points......Page 276
   Curve Sketching......Page 280
   Point of Diminishing Returns......Page 283
   Exercises 4.2......Page 285
   Introduction......Page 290
   L'Hôpital's Rule and the Indeterminate Form 0,0......Page 292
   One-Sided Limits and Limits at ∞......Page 295
   L'Hôpital's Rule and the Indeterminate Form ∞ / ∞ ......Page 296
   Exercises 4.3......Page 298
   Modifying the Graphing Strategy......Page 299
   Using the Graphing Strategy......Page 300
   Modeling Average Cost......Page 306
   Exercises 4.4......Page 308
   Absolute Maxima and Minima......Page 312
   Second Derivative and Extrema......Page 315
   Exercises 4.5......Page 318
   Area and Perimeter......Page 320
   Maximizing Revenue and Profit......Page 323
   Exercises 4.6......Page 329
  Chapter 4: Summary and Review......Page 333
  Review Exercises......Page 334
 Chapter 5: Integration......Page 338
   Antiderivatives......Page 339
   Indefinite Integrals: Formulas and Properties......Page 340
   Applications......Page 345
   Exercises 5.1......Page 347
  5.2 Integration by Substitution......Page 350
   Integration by Substitution......Page 352
   Additional Substitution Techniques......Page 355
   Application......Page 358
   Exercises 5.2......Page 359
  5.3 Differential Equations; Growth and Decay......Page 361
   Differential Equations and Slope Fields......Page 362
   Exponential Growth Law......Page 364
   Population Growth, Radioactive Decay, and Learning......Page 365
   Comparison of Exponential Growth Phenomena......Page 367
   Exercises 5.3......Page 368
   Approximating Areas by Left and Right Sums......Page 372
   The Definite Integral as a Limit of Sums......Page 375
   Properties of the Definite Integral......Page 377
   Exercises 5.4......Page 379
   Introduction to the Fundamental Theorem......Page 382
   Evaluating Definite Integrals......Page 384
   Recognizing a Definite Integral: Average Value......Page 388
   Exercises 5.5......Page 390
  Chapter 5: Summary and Review......Page 394
  Review Exercises......Page 396
 Chapter 6: Additional Integration Topics......Page 400
   Area Between Two Curves......Page 401
   Application: Income Distribution......Page 405
   Exercises 6.1......Page 407
   Probability Density Functions......Page 410
   Continuous Income Stream......Page 412
   Future Value of a Continuous Income Stream......Page 414
   Consumers' and Producers' Surplus......Page 416
   Exercises 6.2......Page 419
  6.3 Integration by Parts......Page 422
   Exercises 6.3......Page 426
  6.4 Other Integration Methods......Page 428
   The Trapezoidal Rule......Page 429
   Simpson's Rule......Page 430
   Using a Table of Integrals......Page 432
   Substitution and Integral Tables......Page 433
   Reduction Formulas......Page 434
   Exercises 6.4......Page 436
  Chapter 6: Summary and Review......Page 439
  Review Exercises......Page 440
 Chapter 7: Multivariable Calculus......Page 443
   Functions of Two or More Independent Variables......Page 444
   Three-Dimensional Coordinate Systems......Page 447
   Exercises 7.1......Page 450
   Partial Derivatives......Page 453
   Second-Order Partial Derivatives......Page 456
   Exercises 7.2......Page 458
  7.3 Maxima and Minima......Page 462
   Exercises 7.3......Page 468
   Functions of Two Independent Variables......Page 470
   Functions of Three Independent Variables......Page 475
   Exercises 7.4......Page 477
   Least Squares Approximation......Page 479
   Exercises 7.5......Page 487
   Introduction......Page 489
   Definition of the Double Integral......Page 492
   Average Value over Rectangular Regions......Page 494
   Volume and Double Integrals......Page 495
   Exercises 7.6......Page 496
   Regular Regions......Page 499
   Double Integrals over Regular Regions......Page 502
   Reversing the Order of Integration......Page 504
   Volume and Double Integrals......Page 505
   Exercises 7.7......Page 506
  Chapter 7: Summary and Review......Page 507
  Review Exercises......Page 510
 Chapter 8: Trigonometric Functions......Page 513
   Angles: Degree—Radian Measure......Page 514
   Trigonometric Functions......Page 515
   Graphs of the Sine and Cosine Functions......Page 517
   Four Other Trigonometric Functions......Page 518
   Exercises 8.1......Page 519
   Derivative Formulas......Page 521
   Exercises 8.2......Page 524
  8.3 Integration of Trigonometric Functions......Page 526
   Exercises 8.3......Page 529
  Chapter 8: Summary and Review......Page 531
  Review Exercises......Page 532
   Set of Real Numbers......Page 533
   Basic Real Number Properties......Page 534
   Further Properties......Page 536
   Exercises A.1......Page 537
   Natural Number Exponents......Page 539
   Combining Like Terms......Page 540
   Addition and Subtraction......Page 541
   Multiplication......Page 542
   Combined Operations......Page 543
   Exercises A.2......Page 544
   Common Factors......Page 545
   Factoring by Grouping......Page 546
   Factoring Second-Degree Polynomials......Page 547
   Special Factoring Formulas......Page 548
   Exercises A.3......Page 550
   Reducing to Lowest Terms......Page 551
   Multiplication and Division......Page 552
   Addition and Subtraction......Page 553
   Compound Fractions......Page 554
   Exercises A.4......Page 555
   Integer Exponents......Page 557
   Scientific Notation......Page 558
   Exercises A.5......Page 560
   n th Roots of Real Numbers......Page 561
   Rational Exponents and Radicals......Page 562
   Properties of Radicals......Page 564
   Exercises A.6......Page 565
  A.7 Quadratic Equations......Page 567
   Quadratic Formula......Page 569
   Quadratic Formula and Factoring......Page 572
   Application: Supply and Demand......Page 573
   Exercises A.7......Page 574
   Sequences......Page 576
   Series and Summation Notation......Page 578
   Exercises B.1......Page 580
   Arithmetic and Geometric Sequences......Page 582
   Sum Formulas for Finite Arithmetic Series......Page 584
   Sum Formulas for Finite Geometric Series......Page 585
   Sum Formula for Infinite Geometric Series......Page 586
   Exercises B.2......Page 587
  B.3 Binomial Theorem......Page 588
   Factorial......Page 589
   Development of the Binomial Theorem......Page 590
   Exercises B.3......Page 591
 Appendix C: Tables......Page 592
  Answers......Page 596
  Index......Page 630
  Index of Applications......Page 638