This is a solution for James Stewart's Calculus (single variable). Covering from chapter 1 to chapter 11. For those who are willing to purchase chapters covering from chapter 12 to chapter 17 please see the other item in my account!
Solution Manual for Calculus 8th Edition / All Chapters 1 - 17 / Full Complete 2023
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SINGLE VARIABLE CALCULUS
EIGHTH EDITION
DANIEL ANDERSON
University of Iowa
JEFFERY A. COLE
Anoka-Ramsey Community College
DANIEL DRUCKER
Wayne State University
Australia . Brazil . Mexico . Singapore . United Kingdom . United States
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Printed in the United States of America
Print Number: 01 Print Year: 2015
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, ■ PREFACE
This Student Solutions Manual contains strategies for solving and solutions to selected exercises
in the text Single Variable Calculus, Eighth Edition, by James Stewart. It contains solutions to the
odd-numbered exercises in each section, the review sections, the True-False Quizzes, and the
Problem Solving sections.
This manual is a text supplement and should be read along with the text. You should read all
exercise solutions in this manual because many concept explanations are given and then used in
subsequent solutions. All concepts necessary to solve a particular problem are not reviewed for
every exercise. If you are having difficulty with a previously covered concept, refer back to the
section where it was covered for more complete help.
A significant number of today’s students are involved in various outside activities, and find it
difficult, if not impossible, to attend all class sessions; this manual should help meet the needs of
these students. In addition, it is our hope that this manual’s solutions will enhance the understand-
ing of all readers of the material and provide insights to solving other exercises.
We use some nonstandard notation in order to save space. If you see a symbol that you don’t
recognize, refer to the Table of Abbreviations and Symbols on page v.
We appreciate feedback concerning errors, solution correctness or style, and manual style. Any
comments may be sent directly to jeff-cole@comcast.net, or in care of the publisher: Cengage
Learning, 20 Channel Center Street, Boston MA 02210.
We would like to thank Kira Abdallah, Kristina Elliott, Stephanie Kuhns, and Kathi Townes,
of TECHarts, for their production services; and Samantha Lugtu, of Cengage Learning, for her
patience and support. All of these people have provided invaluable help in creating this manual.
Jeffery A. Cole
Anoka-Ramsey Community College
James Stewart
McMaster University
and University of Toronto
Daniel Drucker
Wayne State University
Daniel Anderson
University of Iowa
iii
Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
, Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
, ■ ABBREVIATIONS AND SYMBOLS
CD concave downward
CU concave upward
D the domain of f
FDT First Derivative Test
HA horizontal asymptote(s)
I interval of convergence
IP inflection point(s)
R radius of convergence
VA vertical asymptote(s)
CAS
= indicates the use of a computer algebra system.
PR
1 indicates the use of the Product Rule.
QR
1 indicates the use of the Quotient Rule.
CR
1 indicates the use of the Chain Rule.
H
= indicates the use of l’Hospital’s Rule.
j
= indicates the use of Formula j in the Table of Integrals in the back endpapers.
s
= indicates the use of the substitution {u 苷 sin x, du 苷 cos x dx}.
c
= indicates the use of the substitution {u 苷 cos x, du 苷 ⫺sin x dx}.
v
Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
, Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
, ■ CONTENTS
■ DIAGNOSTIC TESTS 1
1 ■ FUNCTIONS AND LIMITS 9
1.1 Four Ways to Represent a Function 9
1.2 Mathematical Models: A Catalog of Essential Functions 14
1.3 New Functions from Old Functions 18
1.4 The Tangent and Velocity Problems 25
1.5 The Limit of a Function 27
1.6 Calculating Limits Using the Limit Laws 32
1.7 The Precise Definition of a Limit 37
1.8 Continuity 41
Review 47
Principles of Problem Solving 53
2 ■ DERIVATIVES 57
2.1 Derivatives and Rates of Change 57
2.2 The Derivative as a Function 63
2.3 Differentiation Formulas 70
2.4 Derivatives of Trigonometric Functions 77
2.5 The Chain Rule 80
2.6 Implicit Differentiation 86
2.7 Rates of Change in the Natural and Social Sciences 92
2.8 Related Rates 97
2.9 Linear Approximations and Differentials 101
Review 104
Problems Plus 113
vii
Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
, viii ■ CONTENTS
3 ■ APPLICATIONS OF DIFFERENTIATION 119
3.1 Maximum and Minimum Values 119
3.2 The Mean Value Theorem 124
3.3 How Derivatives Affect the Shape of a Graph 127
3.4 Limits at Infinity; Horizontal Asymptotes 137
3.5 Summary of Curve Sketching 144
3.6 Graphing with Calculus and Calculators 154
3.7 Optimization Problems 162
3.8 Newton’s Method 174
3.9 Antiderivatives 178
Review 183
Problems Plus 193
4 ■ INTEGRALS 199
4.1 Areas and Distances 199
4.2 The Definite Integral 205
4.3 The Fundamental Theorem of Calculus 211
4.4 Indefinite Integrals and the Net Change Theorem 216
4.5 The Substitution Rule 219
Review 224
Problems Plus 229
5 ■ APPLICATIONS OF INTEGRATION 233
5.1 Areas Between Curves 233
5.2 Volumes 240
5.3 Volumes by Cylindrical Shells 248
5.4 Work 253
5.5 Average Value of a Function 256
Review 257
Problems Plus 261
Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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