Calculus with applications

Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
Contents......Page 6
Preface......Page 10
Prerequisite Skills Diagnostic Test......Page 20
Chapter R: Algebra Reference......Page 22
 R.1. Polynomials......Page 23
 R.2. Factoring......Page 26
 R.3. Rational Expressions......Page 29
 R.4. Equations......Page 32
 R.5. Inequalities......Page 38
 R.6. Exponents......Page 42
 R.7. Radicals......Page 47
Chapter 1: Linear Functions......Page 52
 1.1. Slopes and Equations of Lines......Page 53
 1.2. Linear Functions and Applications......Page 68
 1.3. The Least Squares Line......Page 78
  Chapter 1: Review......Page 91
  Extended Application: Using Extrapolation to Predict Life Expectancy......Page 97
Chapter 2: Nonlinear Functions......Page 99
 2.1. Properties of Functions......Page 100
 2.2. Quadratic Functions; Translation and Reflection......Page 113
 2.3. Polynomial and Rational Functions......Page 127
 2.4. Exponential Functions......Page 140
 2.5. Logarithmic Functions......Page 151
 2.6. Applications: Growth and Decay; Mathematics of Finance......Page 164
  Chapter 2: Review......Page 172
  Extended Application: Power Functions......Page 180
Chapter 3: The Derivative......Page 184
 3.1. Limits......Page 185
 3.2. Continuity......Page 203
 3.3. Rates of Change......Page 212
 3.4. Definition of the Derivative......Page 225
 3.5. Graphical Differentiation......Page 244
  Chapter 3: Review......Page 251
  Extended Application: A Model for Drugs Administered Intravenously......Page 257
Chapter 4: Calculating the Derivative......Page 260
 4.1. Techniques for Finding Derivatives......Page 261
 4.2. Derivatives of Products and Quotients......Page 277
 4.3. The Chain Rule......Page 284
 4.4. Derivatives of Exponential Functions......Page 294
 4.5. Derivatives of Logarithmic Functions......Page 302
  Chapter 4: Review......Page 309
  Extended Application: Electric Potential and Electric Field......Page 314
Chapter 5: Graphs and the Derivative......Page 317
 5.1. Increasing and Decreasing Functions......Page 318
 5.2. Relative Extrema......Page 329
 5.3. Higher Derivatives, Concavity, and the Second Derivative Test......Page 341
 5.4. Curve Sketching......Page 356
  Chapter 5: Review......Page 365
  Extended Application: A Drug Concentration Model for Orally Administered Medications......Page 369
Chapter 6: Applications of the Derivative......Page 372
 6.1. Absolute Extrema......Page 373
 6.2. Applications of Extrema......Page 382
 6.3. Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand......Page 392
 6.4. Implicit Differentiation......Page 401
 6.5. Related Rates......Page 407
 6.6. Differentials: Linear Approximation......Page 414
  Chapter 6: Review......Page 420
  Extended Application: A Total Cost Model for a Training Program......Page 424
Chapter 7: Integration......Page 426
 7.1. Antiderivatives......Page 427
 7.2. Substitution......Page 439
 7.3. Area and the Definite Integral......Page 447
 7.4. The Fundamental Theorem of Calculus......Page 459
 7.5. The Area Between Two Curves......Page 469
 7.6. Numerical Integration......Page 478
  Chapter 7: Review......Page 487
  Extended Application: Estimating Depletion Dates for Minerals......Page 492
Chapter 8: Further Techniques and Applications of Integration......Page 496
 8.1. Integration by Parts......Page 497
 8.2. Volume and Average Value......Page 506
 8.3. Continuous Money Flow......Page 513
 8.4. Improper Integrals......Page 521
  Chapter 8: Review......Page 527
  Extended Application: Estimating Learning Curves in Manufacturing with Integrals......Page 530
Chapter 9: Multivariable Calculus......Page 533
 9.1. Functions of Several Variables......Page 534
 9.2. Partial Derivatives......Page 545
 9.3. Maxima and Minima......Page 557
 9.4. Lagrange Multipliers......Page 566
 9.5. Total Differentials and Approximations......Page 575
 9.6. Double Integrals......Page 580
  Chapter 9: Review......Page 591
  Extended Application: Using Multivariable Fitting to Create a Response Surface Design......Page 597
Chapter 10: Differential Equations......Page 601
 10.1. Solutions of Elementary and Separable Differential Equations......Page 602
 10.2. Linear First-Order Differential Equations......Page 616
 10.3. Euler’s Method......Page 622
 10.4. Applications of Differential Equations......Page 629
  Chapter 10: Review......Page 637
  Extended Application: Pollution of the Great Lakes......Page 642
Chapter 11: Probability and Calculus......Page 645
 11.1. Continuous Probability Models......Page 646
 11.2. Expected Value and Variance of Continuous Random Variables......Page 657
 11.3. Special Probability Density Functions......Page 667
  Chapter 11: Review......Page 680
  Extended Application: Exponential Waiting Times......Page 685
Chapter 12: Sequences and Series......Page 688
 12.1. Geometric Sequences......Page 689
 12.2. Annuities: An Application of Sequences......Page 694
 12.3. Taylor Polynomials at 0......Page 704
 12.4. Infinite Series......Page 713
 12.5. Taylor Series......Page 720
 12.6. Newton’s Method......Page 729
 12.7. L’Hospital’s Rule......Page 734
  Chapter 12: Review......Page 741
  Extended Application: Living Assistance and Subsidized Housing......Page 744
Chapter 13: The Trigonometric Functions......Page 746
 13.1. Definitions of the Trigonometric Functions......Page 747
 13.2. Derivatives of Trigonometric Functions......Page 763
 13.3. Integrals of Trigonometric Functions......Page 775
  Chapter 13: Review......Page 783
  Extended Application: The Shortest Time and the Cheapest Path......Page 789
Appendix A: Solutions to Prerequisite Skills Diagnostic Test......Page 792
Appendix B: Tables......Page 795
Answers to Selected Exercises......Page 800
Credits......Page 836
Index of Applications......Page 838
Index......Page 842
Sources......Page 850
Key Definitions, Theorems, and Formulas......Page 862
Back Cover......Page 866