Calculus with Applications, Brief Version – 12th
Edition
ST
INSTRUCTOR’S
UV
RESOURCE &
IA
SOLUTIONS MANUAL
_A
PP
Margaret L. Lial
Raymond N. Greenwell
RO
Nathan P. Ritchey
VE
Comprehensive Resource and Solutions Manual
D?
for Instructors and Students
??
© Margaret L. Lial, Raymond N. Greenwell & Nathan P. Ritchey
All rights reserved. Reproduction or distribution without permission is prohibited.
©STUDYSTREAM
, CONTENTS
PREFACE................................................................................................................................................................... ix
ST
HINTS FOR TEACHING CALCULUS WITH APPLICATIONS ............................................................................ xi
PRETESTS ................................................................................................................................................................. xix
UV
ANSWERS TO PRETESTS ....................................................................................................................................... xxvii
FINAL EXAMINATIONS ......................................................................................................................................... xxix
ANSWERS TO FINAL EXAMINATIONS............................................................................................................... xliii
IA
SOLUTIONS TO ALL EXERCISES
_A
CHAPTER R ALGEBRA REFERENCE
R.1 Polynomials .................................................................................................................................................. 1
PP
R.2 Factoring ....................................................................................................................................................... 3
R.3 Rational Expressions .................................................................................................................................... 4
R.4 Equations ...................................................................................................................................................... 8
RO
R.5 Inequalities ................................................................................................................................................... 14
R.6 Exponents ..................................................................................................................................................... 24
R.7 Radicals ........................................................................................................................................................ 28
VE
CHAPTER 1 LINEAR FUNCTIONS
1.1 Slopes and Equations of Lines ...................................................................................................................... 33
D?
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
Copyright © 2022 Pearson Education, Inc. iii
, CHAPTER 2 NONLINEAR FUNCTIONS
2.1 Properties of Functions.................................................................................................................................. 77
2.2 Quadratic Functions; Translation and Reflection .......................................................................................... 86
ST
2.3 Polynomial and Rational Functions .............................................................................................................. 102
2.4 Exponential Functions ................................................................................................................................... 115
2.5 Logarithmic Functions .................................................................................................................................. 125
UV
2.6 Applications: Growth and Decay; Mathematics of Finance .......................................................................... 137
Chapter 2 Review Exercises.................................................................................................................................. 146
Extended Application: Power Functions ............................................................................................................... 162
IA
CHAPTER 3 THE DERIVATIVE
3.1 Limits ............................................................................................................................................................ 163
_A
3.2 Continuity...................................................................................................................................................... 177
3.3 Rates of Change ............................................................................................................................................ 184
3.4 Definition of the Derivative .......................................................................................................................... 195
3.5 Graphical Differentiation .............................................................................................................................. 219
PP
Chapter 3 Review Exercises.................................................................................................................................. 223
Extended Application: A Model for Drugs Administered Intravenously .............................................................. 235
RO
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
VE
4.4 Derivatives of Exponential Functions ........................................................................................................... 269
4.5 Derivatives of Logarithmic Functions ........................................................................................................... 283
Chapter 4 Review Exercises.................................................................................................................................. 296
D?
Extended Application: Electric Potential and Electric Field ................................................................................. 308
??
iv Copyright © 2022 Pearson Education, Inc. CONTENTS
, CHAPTER 5 GRAPHS AND THE DERIVATIVE
5.1 Increasing and Decreasing Functions ............................................................................................................ 309
5.2 Relative Extrema ........................................................................................................................................... 324
ST
5.3 Higher Derivatives, Concavity, and the Second Derivative Test .................................................................. 339
5.4 Curve Sketching ............................................................................................................................... 362
Chapter 5 Review Exercises.................................................................................................................................. 383
UV
Extended Application: A Drug Concentration Model for Orally Administered Medications ............................... 400
CHAPTER 6 APPLICATIONS OF THE DERIVATIVE
6.1 Absolute Extrema .......................................................................................................................................... 401
IA
6.2 Applications of Extrema................................................................................................................................ 411
6.3 Further Business Applications....................................................................................................................... 432
_A
6.4 Implicit Differentiation ................................................................................................................................. 440
6.5 Related Rates ................................................................................................................................................. 457
6.6 Differentials: Linear Approximation ............................................................................................................. 466
Chapter 6 Review Exercises.................................................................................................................................. 472
PP
Extended Application: A Total Cost Model for a Training Program .................................................................... 483
CHAPTER 7 INTEGRATION
RO
7.1 Antiderivatives .............................................................................................................................................. 485
7.2 Substitution ................................................................................................................................................... 497
7.3 Area and the Definite Integral ....................................................................................................................... 507
7.4 The Fundamental Theorem of Calculus ........................................................................................................ 521
VE
7.5 The Area Between Two Curves .................................................................................................................... 538
7.6 Numerical Integration ................................................................................................................................... 556
Chapter 7 Review Exercises.................................................................................................................................. 570
D?
Extended Application: Estimating Depletion Dates for Minerals ......................................................................... 588
??
CONTENTS Copyright © 2022 Pearson Education, Inc. v
Edition
ST
INSTRUCTOR’S
UV
RESOURCE &
IA
SOLUTIONS MANUAL
_A
PP
Margaret L. Lial
Raymond N. Greenwell
RO
Nathan P. Ritchey
VE
Comprehensive Resource and Solutions Manual
D?
for Instructors and Students
??
© Margaret L. Lial, Raymond N. Greenwell & Nathan P. Ritchey
All rights reserved. Reproduction or distribution without permission is prohibited.
©STUDYSTREAM
, CONTENTS
PREFACE................................................................................................................................................................... ix
ST
HINTS FOR TEACHING CALCULUS WITH APPLICATIONS ............................................................................ xi
PRETESTS ................................................................................................................................................................. xix
UV
ANSWERS TO PRETESTS ....................................................................................................................................... xxvii
FINAL EXAMINATIONS ......................................................................................................................................... xxix
ANSWERS TO FINAL EXAMINATIONS............................................................................................................... xliii
IA
SOLUTIONS TO ALL EXERCISES
_A
CHAPTER R ALGEBRA REFERENCE
R.1 Polynomials .................................................................................................................................................. 1
PP
R.2 Factoring ....................................................................................................................................................... 3
R.3 Rational Expressions .................................................................................................................................... 4
R.4 Equations ...................................................................................................................................................... 8
RO
R.5 Inequalities ................................................................................................................................................... 14
R.6 Exponents ..................................................................................................................................................... 24
R.7 Radicals ........................................................................................................................................................ 28
VE
CHAPTER 1 LINEAR FUNCTIONS
1.1 Slopes and Equations of Lines ...................................................................................................................... 33
D?
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
Copyright © 2022 Pearson Education, Inc. iii
, CHAPTER 2 NONLINEAR FUNCTIONS
2.1 Properties of Functions.................................................................................................................................. 77
2.2 Quadratic Functions; Translation and Reflection .......................................................................................... 86
ST
2.3 Polynomial and Rational Functions .............................................................................................................. 102
2.4 Exponential Functions ................................................................................................................................... 115
2.5 Logarithmic Functions .................................................................................................................................. 125
UV
2.6 Applications: Growth and Decay; Mathematics of Finance .......................................................................... 137
Chapter 2 Review Exercises.................................................................................................................................. 146
Extended Application: Power Functions ............................................................................................................... 162
IA
CHAPTER 3 THE DERIVATIVE
3.1 Limits ............................................................................................................................................................ 163
_A
3.2 Continuity...................................................................................................................................................... 177
3.3 Rates of Change ............................................................................................................................................ 184
3.4 Definition of the Derivative .......................................................................................................................... 195
3.5 Graphical Differentiation .............................................................................................................................. 219
PP
Chapter 3 Review Exercises.................................................................................................................................. 223
Extended Application: A Model for Drugs Administered Intravenously .............................................................. 235
RO
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
VE
4.4 Derivatives of Exponential Functions ........................................................................................................... 269
4.5 Derivatives of Logarithmic Functions ........................................................................................................... 283
Chapter 4 Review Exercises.................................................................................................................................. 296
D?
Extended Application: Electric Potential and Electric Field ................................................................................. 308
??
iv Copyright © 2022 Pearson Education, Inc. CONTENTS
, CHAPTER 5 GRAPHS AND THE DERIVATIVE
5.1 Increasing and Decreasing Functions ............................................................................................................ 309
5.2 Relative Extrema ........................................................................................................................................... 324
ST
5.3 Higher Derivatives, Concavity, and the Second Derivative Test .................................................................. 339
5.4 Curve Sketching ............................................................................................................................... 362
Chapter 5 Review Exercises.................................................................................................................................. 383
UV
Extended Application: A Drug Concentration Model for Orally Administered Medications ............................... 400
CHAPTER 6 APPLICATIONS OF THE DERIVATIVE
6.1 Absolute Extrema .......................................................................................................................................... 401
IA
6.2 Applications of Extrema................................................................................................................................ 411
6.3 Further Business Applications....................................................................................................................... 432
_A
6.4 Implicit Differentiation ................................................................................................................................. 440
6.5 Related Rates ................................................................................................................................................. 457
6.6 Differentials: Linear Approximation ............................................................................................................. 466
Chapter 6 Review Exercises.................................................................................................................................. 472
PP
Extended Application: A Total Cost Model for a Training Program .................................................................... 483
CHAPTER 7 INTEGRATION
RO
7.1 Antiderivatives .............................................................................................................................................. 485
7.2 Substitution ................................................................................................................................................... 497
7.3 Area and the Definite Integral ....................................................................................................................... 507
7.4 The Fundamental Theorem of Calculus ........................................................................................................ 521
VE
7.5 The Area Between Two Curves .................................................................................................................... 538
7.6 Numerical Integration ................................................................................................................................... 556
Chapter 7 Review Exercises.................................................................................................................................. 570
D?
Extended Application: Estimating Depletion Dates for Minerals ......................................................................... 588
??
CONTENTS Copyright © 2022 Pearson Education, Inc. v
