Type:
Instructor Manual and Resource
Resource:
Calculus with Applications
Edition:
12th Edition
Author(s):
Margaret L. Lial Nathan P. Ritchey Raymond N. Greenwell
CONTENTS PREFACE...................................................................................................................................................................
ix
HINTS FOR TEACHING CALCULUS WITH APPLICATIONS ............................................................................
xi
PRETESTS ................................................................................................................................................................. xix ANSWERS TO PRETESTS ....................................................................................................................................... xxvii FINAL EXAMINATIONS ......................................................................................................................................... xxix ANSWERS TO FINAL EXAMINATIONS............................................................................................................... xliii
SOLUTIONS TO ALL EXERCISES CHAPTER R ALGEBRA REFERENCE R.1 Polynomials ..................................................................................................................................................
1
R.2 Factoring .......................................................................................................................................................
3
R.3 Rational Expressions ....................................................................................................................................
4
R.4 Equations ......................................................................................................................................................
8
R.5 Inequalities ...................................................................................................................................................
14
R.6 Exponents .....................................................................................................................................................
24
R.7 Radicals ........................................................................................................................................................
28
CHAPTER 1 LINEAR FUNCTIONS 1.1 Slopes and Equations of Lines ......................................................................................................................
33
1.2 Linear Functions and Applications................................................................................................................
46
1.3 The Least Squares Line .................................................................................................................................
54
Chapter 1 Review Exercises..................................................................................................................................
66
Extended Application: Predicting Life Expectancy ..............................................................................................
74
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CHAPTER 2 NONLINEAR FUNCTIONS 2.1 Properties of Functions..................................................................................................................................
77
2.2 Quadratic Functions; Translation and Reflection ..........................................................................................
86
2.3 Polynomial and Rational Functions .............................................................................................................. 102 2.4 Exponential Functions ................................................................................................................................... 115 2.5 Logarithmic Functions .................................................................................................................................. 125 2.6 Applications: Growth and Decay; Mathematics of Finance .......................................................................... 137 Chapter 2 Review Exercises.................................................................................................................................. 146 Extended Application: Power Functions ............................................................................................................... 162
CHAPTER 3 THE DERIVATIVE 3.1 Limits ............................................................................................................................................................ 163 3.2 Continuity...................................................................................................................................................... 177 3.3 Rates of Change ............................................................................................................................................ 184 3.4 Definition of the Derivative .......................................................................................................................... 195 3.5 Graphical Differentiation .............................................................................................................................. 219 Chapter 3 Review Exercises.................................................................................................................................. 223 Extended Application: A Model for Drugs Administered Intravenously .............................................................. 235
CHAPTER 4 CALCULATING THE DERIVATIVE 4.1 Techniques for Finding Derivatives .............................................................................................................. 237 4.2 Derivatives of Products and Quotients .......................................................................................................... 247 4.3 The Chain Rule ............................................................................................................................................. 258 4.4 Derivatives of Exponential Functions ........................................................................................................... 269 4.5 Derivatives of Logarithmic Functions ........................................................................................................... 283 Chapter 4 Review Exercises.................................................................................................................................. 296 Extended Application: Electric Potential and Electric Field ................................................................................. 308
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CONTENTS
CHAPTER 5 GRAPHS AND THE DERIVATIVE 5.1 Increasing and Decreasing Functions ............................................................................................................ 309 5.2 Relative Extrema ........................................................................................................................................... 324 5.3 Higher Derivatives, Concavity, and the Second Derivative Test .................................................................. 339 5.4 Curve Sketching
............................................................................................................................... 362
Chapter 5 Review Exercises.................................................................................................................................. 383 Extended Application: A Drug Concentration Model for Orally Administered Medications ............................... 400
CHAPTER 6 APPLICATIONS OF THE DERIVATIVE 6.1 Absolute Extrema .......................................................................................................................................... 401 6.2 Applications of Extrema................................................................................................................................ 411 6.3 Further Business Applications....................................................................................................................... 432 6.4 Implicit Differentiation ................................................................................................................................. 440 6.5 Related Rates ................................................................................................................................................. 457 6.6 Differentials: Linear Approximation ............................................................................................................. 466 Chapter 6 Review Exercises.................................................................................................................................. 472 Extended Application: A Total Cost Model for a Training Program .................................................................... 483
CHAPTER 7 INTEGRATION 7.1 Antiderivatives .............................................................................................................................................. 485 7.2 Substitution ................................................................................................................................................... 497 7.3 Area and the Definite Integral ....................................................................................................................... 507 7.4 The Fundamental Theorem of Calculus ........................................................................................................ 521 7.5 The Area Between Two Curves .................................................................................................................... 538 7.6 Numerical Integration ................................................................................................................................... 556 Chapter 7 Review Exercises.................................................................................................................................. 570 Extended Application: Estimating Depletion Dates for Minerals ......................................................................... 588
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CHAPTER 8 FURTHER TECHNIQUES AND APPLICATIONS OF INTEGRATION 8.1 Integration by Parts ....................................................................................................................................... 589 8.2 Volume and Average Value .......................................................................................................................... 601 8.3 Continuous Money Flow ............................................................................................................................... 612 8.4 Improper Integrals ......................................................................................................................................... 619 Chapter 8 Review Exercises.................................................................................................................................. 633 Extended Application: Estimating Learning Curves in Manufacturing with Integrals ......................................... 643
CHAPTER 9 MULTIVARIABLE CALCULUS 9.1 Functions of Several Variables...................................................................................................................... 645 9.2 Partial Derivatives ........................................................................................................................................ 655 9.3 Maxima and Minima ..................................................................................................................................... 671 9.4 Lagrange Multipliers ..................................................................................................................................... 686 9.5 Total Differentials and Approximations ........................................................................................................ 702 9.6 Double Integrals ............................................................................................................................................ 711 Chapter 9 Review Exercises.................................................................................................................................. 730 Extended Application: Using Multivariable Fitting to Create a Response Surface Design .................................. 749
CHAPTER 10 DIFFERENTIAL EQUATIONS 10.1 Solutions of Elementary and Separable Differential Equations .................................................................. 751 10.2 Linear First-Order Differential Equations ................................................................................................... 769 10.3 Euler’s Method ............................................................................................................................................ 778 10.4 Applications of Differential Equations........................................................................................................ 788 Chapter 10 Review Exercises ............................................................................................................................... 800 Extended Application: Pollution of a Lake ........................................................................................................... 813
CHAPTER 11 PROBABILITY AND CALCULUS 11.1 Continuous Probability Models ................................................................................................................... 815 11.2 Expected Value and Variance of Continuous Random Variables ............................................................... 828 11.3 Special Probability Density Functions ........................................................................................................ 845 Chapter 11 Review Exercises ................................................................................................................................ 857 Extended Application: Exponential Waiting Times .............................................................................................. 871 vi
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CONTENTS