Calculus & Its Applications (th Edition)

Cover......Page 1
Inside Front Cover......Page 2
Title Page......Page 4
Copyright Page......Page 5
Contents......Page 6
Preface......Page 10
Acknowledgments......Page 19
Acknowledgments for the Global Edition......Page 20
Prerequisite Skills Diagnostic Test......Page 21
Introduction......Page 23
 0.1 Functions and Their Graphs......Page 24
 0.2 Some Important Functions......Page 34
 0.3 The Algebra of Functions......Page 42
 0.4 Zeros of Functions—The Quadratic Formula and Factoring......Page 47
 0.5 Exponents and Power Functions......Page 55
 0.6 Functions and Graphs in Applications......Page 63
 Chapter Summary and Chapter Review Exercises......Page 73
1 The Derivative......Page 79
 1.1 The Slope of a Straight Line......Page 80
 1.2 The Slope of a Curve at a Point......Page 89
 1.3 The Derivative and Limits......Page 95
 1.4 Limits and the Derivative......Page 105
 1.5 Differentiability and Continuity......Page 114
 1.6 Some Rules for Differentiation......Page 120
 1.7 More about Derivatives......Page 127
 1.8 The Derivative as a Rate of Change......Page 135
 Chapter Summary and Chapter Review Exercises......Page 146
 2.1 Describing Graphs of Functions......Page 154
 2.2 The First- and Second-Derivative Rules......Page 164
 2.3 The First- and Second-Derivative Tests and Curve Sketching......Page 171
 2.4 Curve Sketching (Conclusion)......Page 181
 2.5 Optimization Problems......Page 186
 2.6 Further Optimization Problems......Page 193
 2.7 Applications of Derivatives to Business and Economics......Page 201
 Chapter Summary and Chapter Review Exercises......Page 209
 3.1 The Product and Quotient Rules......Page 216
 3.2 The Chain Rule......Page 225
 *3.3 Implicit Differentiation and Related Rates......Page 232
 Chapter Summary and Chapter Review Exercises......Page 241
 4.1 Exponential Functions......Page 245
 4.2 The Exponential Function ex......Page 249
 4.3 Differentiation of Exponential Functions......Page 255
 4.4 The Natural Logarithm Function......Page 260
 4.5 The Derivative of ln x......Page 264
 4.6 Properties of the Natural Logarithm Function......Page 269
 Chapter Summary and Chapter Review Exercises......Page 273
 5.1 Exponential Growth and Decay......Page 277
 5.2 Compound Interest......Page 288
 5.3 Applications of the Natural Logarithm Function to Economics......Page 294
 5.4 Further Exponential Models......Page 301
 Chapter Summary and Chapter Review Exercises......Page 311
6 The Definite Integral......Page 315
 6.1 Antidifferentiation......Page 316
 6.2 The Definite Integral and Net Change of a Function......Page 325
 6.3 The Definite Integral and Area under a Graph......Page 332
 6.4 Areas in the xy-Plane......Page 342
 6.5 Applications of the Definite Integral......Page 355
 Chapter Summary and Chapter Review Exercises......Page 363
 7.1 Examples of Functions of Several Variables......Page 371
 7.2 Partial Derivatives......Page 377
 7.3 Maxima and Minima of Functions of Several Variables......Page 385
 7.4 Lagrange Multipliers and Constrained Optimization......Page 393
 7.5 The Method of Least Squares......Page 401
 7.6 Double Integrals......Page 407
 Chapter Summary and Chapter Review Exercises......Page 412
 8.1 Radian Measure of Angles......Page 417
 8.2 The Sine and the Cosine......Page 420
 8.3 Differentiation and Integration of sin t and cos t......Page 426
 8.4 The Tangent and Other Trigonometric Functions......Page 434
 Chapter Summary and Chapter Review Exercises......Page 438
9 Techniques of Integration......Page 443
 9.1 Integration by Substitution......Page 444
 9.2 Integration by Parts......Page 450
 9.3 Evaluation of Definite Integrals......Page 454
 9.4 Approximation of Definite Integrals......Page 458
 9.5 Some Applications of the Integral......Page 467
 9.6 Improper Integrals......Page 472
 Chapter Summary and Chapter Review Exercises......Page 477
 10.1 Solutions of Differential Equations......Page 483
 10.2 Separation of Variables......Page 491
 10.3 First-Order Linear Differential Equations......Page 498
 10.4 Applications of First-Order Linear Differential Equations......Page 502
 10.5 Graphing Solutions of Differential Equations......Page 509
 10.6 Applications of Differential Equations......Page 517
 10.7 Numerical Solution of Differential Equations......Page 523
 Chapter Summary and Chapter Review Exercises......Page 528
 11.1 Taylor Polynomials......Page 535
 11.2 The Newton–Raphson Algorithm......Page 543
 11.3 Infinite Series......Page 549
 11.4 Series with Positive Terms......Page 557
 11.5 Taylor Series......Page 563
 Chapter Summary and Chapter Review Exercises......Page 570
 12.1 Discrete Random Variables......Page 575
 12.2 Continuous Random Variables......Page 581
 12.3 Expected Value and Variance......Page 588
 12.4 Exponential and Normal Random Variables......Page 593
 12.5 Poisson and Geometric Random Variables......Page 602
 Chapter Summary and Chapter Review Exercises......Page 609
Appendix Areas under the Standard Normal Curve......Page 614
Learning Objectives (Online)......Page 615
Sources......Page 624
Selected Answers......Page 626
Index of Applications......Page 658
 B......Page 660
 D......Page 661
 F......Page 662
 G......Page 663
 J......Page 664
 N......Page 665
 Q......Page 666
 S......Page 667
 W......Page 668
 Z......Page 669
Inside Back Cover......Page 676
Back Cover......Page 677