Calculus with Applications

Cover......Page 1
Title Page......Page 5
Copyright Page......Page 6
Contents......Page 7
Preface......Page 11
A Quick Walk-Through of Calculus with Applications, 10e......Page 15
Supplements......Page 19
Acknowledgments......Page 21
Dear Student......Page 23
Prerequisite Skills Diagnostic Test......Page 24
CHAPTER R: Algebra Reference......Page 27
R.1 Polynomials......Page 28
R.2 Factoring......Page 31
R.3 Rational Expressions......Page 34
R.4 Equations......Page 37
R.5 Inequalities......Page 42
R.6 Exponents......Page 47
R.7 Radicals......Page 51
CHAPTER 1 Linear Functions......Page 57
1.1 Slopes and Equations of Lines......Page 58
1.2 Linear Functions and Applications......Page 73
1.3 The Least Squares Line......Page 81
CHAPTER 1 REVIEW......Page 94
EXTENDED APPLICATION: Using Extrapolation to Predict Life Expectancy......Page 98
CHAPTER 2 Nonlinear Functions......Page 100
2.1 Properties of Functions......Page 101
2.2 Quadratic FunctionsTranslation and Reflection......Page 120
2.3 Polynomial and Rational Functions......Page 123
2.4 Exponential Functions......Page 135
2.5 Logarithmic Functions......Page 145
2.6 Applications: Growth and Decay Mathematics of Finance......Page 158
CHAPTER 2 REVIEW......Page 166
EXTENDED APPLICATION: Power Functions......Page 174
CHAPTER 3 The Derivative......Page 177
3.1 Limits......Page 178
3.2 Continuity......Page 196
3.3 Rates of Change......Page 205
3.4 Definition of the Derivative......Page 218
3.5 Graphical Differentiation......Page 236
CHAPTER 3 REVIEW......Page 242
EXTENDED APPLICATION: A Model for Drugs Administered Intravenously......Page 249
CHAPTER 4 Calculating the Derivative......Page 252
4.1 Techniques for Finding Derivatives......Page 253
4.2 Derivatives of Products and Quotients......Page 267
4.3 The Chain Rule......Page 274
4.4 Derivatives of Exponential Functions......Page 284
4.5 Derivatives of Logarithmic Functions......Page 292
CHAPTER 4 REVIEW......Page 299
EXTENDED APPLICATION: Electric Potential and Electric Field......Page 304
CHAPTER 5 Graphs and the Derivative......Page 307
5.1 Increasing and Decreasing Functions......Page 308
5.2 Relative Extrema......Page 319
5.3 Higher Derivatives, Concavity, and the Second Derivative Test......Page 330
5.4 Curve Sketching......Page 343
CHAPTER 5 REVIEW......Page 352
EXTENDED APPLICATION: A Drug Concentration Model for Orally Administered Medications......Page 356
CHAPTER 6 Applications of the Derivative......Page 359
6.1 Absolute Extrema......Page 360
6.2 Applications of Extrema......Page 369
6.3 Further Business Applications: Economic Lot Size Economic Order Quantity Elasticity of Demand......Page 378
6.4 Implicit Differentiation......Page 387
6.5 Related Rates......Page 392
6.6 Differentials: Linear Approximation......Page 399
CHAPTER 6 REVIEW......Page 405
EXTENDED APPLICATION: A Total Cost Model for a Training Program......Page 409
CHAPTER 7 Integration......Page 411
7.1 Antiderivatives......Page 412
7.2 Substitution......Page 424
7.3 Area and the Definite Integral......Page 432
7.4 The Fundamental Theorem of Calculus......Page 444
7.5 The Area Between Two Curves......Page 454
7.6 Numerical Integration......Page 464
CHAPTER 7 REVIEW......Page 472
EXTENDED APPLICATION: Estimating Depletion Dates for Minerals......Page 477
CHAPTER 8 Further Techniques and Applications of Integration......Page 481
8.1 Integration by Parts......Page 482
8.2 Volume and Average Value......Page 490
8.3 Continuous Money Flow......Page 497
8.4 Improper Integrals......Page 504
CHAPTER 8 REVIEW......Page 510
EXTENDED APPLICATION: Estimating Learning Curves in Manufacturing with Integrals......Page 513
CHAPTER 9 Multivariable Calculus......Page 515
9.1 Functions of Several Variables......Page 516
9.2 Partial Derivatives......Page 527
9.3 Maxima and Minima......Page 538
9.4 Lagrange Multipliers......Page 547
9.5 Total Differentials and Approximations......Page 555
9.6 Double Integrals......Page 560
CHAPTER 9 REVIEW......Page 571
EXTENDED APPLICATION: Using Multivariable Fitting to Create a Response Surface Design......Page 577
CHAPTER 10 Differential Equations......Page 581
10.1 Solutions of Elementary and Separable Differential Equations......Page 582
10.2 Linear First-Order Differential Equations......Page 595
10.3 Euler’s Method......Page 601
10.4 Applications of Differential Equations......Page 607
CHAPTER 10 REVIEW......Page 615
EXTENDED APPLICATION: Pollution of the Great Lakes......Page 620
CHAPTER 11 Probability and Calculus......Page 623
11.1 Continuous Probability Models......Page 624
11.2 Expected Value and Variance of Continuous Random Variables......Page 635
11.3 Special Probability Density Functions......Page 644
CHAPTER 11 REVIEW......Page 656
EXTENDED APPLICATION: Exponential Waiting Times......Page 661
CHAPTER 12 Sequences and Series......Page 664
12.1 Geometric Sequences......Page 665
12.2 Annuities: An Application of Sequences......Page 669
12.3 Taylor Polynomials at 0......Page 680
12.4 Infinite Series......Page 689
12.5 Taylor Series......Page 695
12.6 Newton’s Method......Page 705
12.7 l’Hôpital’s Rule......Page 709
CHAPTER 12 REVIEW......Page 716
EXTENDED APPLICATION: Living Assistance and Subsidized Housing......Page 719
CHAPTER 13 The Trigonometric Functions......Page 721
13.1 Definitions of the Trigonometric Functions......Page 722
13.2 Derivatives of Trigonometric Functions......Page 738
13.3 Integrals of Trigonometric Functions......Page 748
CHAPTER 13 REVIEW......Page 755
EXTENDED APPLICATION: The Shortest Time and the Cheapest Path......Page 760
A: Solutions to Prerequisite Skills Diagnostic Test......Page 763
B: Learning Objectives......Page 766
C: MathPrint Operating System for TI-84 and TI-84 Plus Silver Edition......Page 770
1 Formulas of Geometry......Page 772
2 Area Under a Normal Curve......Page 773
3 Integrals......Page 775
4 Integrals Involving Trigonometric Functions......Page 776
Answers to Selected Exercises......Page 777
Credits......Page 811
R......Page 813
HEALTH AND LIFE SCIENCES......Page 814
PHYSICAL SCIENCES......Page 815
SOCIAL SCIENCES......Page 816
C......Page 817
E......Page 818
G......Page 819
L......Page 820
P......Page 821
S......Page 822
Y......Page 823
Z......Page 824
Sources......Page 825