SOLUTIONS MANUAL
Prepared by
Neil Wigley
University of Windsor
Albert Herr
To Accompany
CALCULUS
EARLY TRANSCENDENTALS
Seventh Edition
Howard Anton
Drexel University
Irl C. Bivens
Davidson College
Stephen L. Davis
Davidson College
John Wiley & Sons, Inc.
,Cover Design: Norm Christensen
To order books or for customer service call 1-800-CALL-WILEY (225-5945).
Copyright 2002 by John Wiley & Sons, Inc.
Excerpts from this work may be reproduced by instructors for
distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for
which the textbook has been adopted. Any other
reproduction or translation of this work beyond that
permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner
is unlawful. Requests for permission or further information
should be addressed to the Permissions Department, John
Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-
0012.
ISBN 0-471-43497-3
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
Printed and bound by Victor Graphics, Inc.
, CONTENTS
Chapter 1. Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 2. Limits and Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Chapter 3. The Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70
Chapter 4. Exponential, Logarithmic, and Inverse Trigonometric Functions . . . 122
Chapter 5. The Derivative in Graphing and Applications . . . . . . . . . . . . . . . . . . . . 150
Chapter 6. Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Chapter 7. Applications of the Definite Integral in Geometry,
Science, and Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .278
Chapter 8. Principles of Integral Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
Chapter 9. Mathematical Modeling with Differential Equations . . . . . . . . . . . . . . 372
Chapter 10. Infinite Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
Chapter 11. Analytic Geometry in Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .447
Chapter 12. Three-Dimensional Space; Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492
Chapter 13. Vector-Valued Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
Chapter 14. Partial Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569
Chapter 15. Multiple Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620
Chapter 16. Topics in Vector Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657
Appendix A. Real Numbers, Intervals, and Inequalities . . . . . . . . . . . . . . . . . . . . . . . 690
Appendix B. Absolute Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697
Appendix C. Coordinate Planes and Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700
Appendix D. Distance, Circles, and Quadratic Equations . . . . . . . . . . . . . . . . . . . . . . 709
Appendix E. Trigonometry Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719
Appendix F. Solving Polynomial Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725
, CHAPTER 1
Functions
EXERCISE SET 1.1
1. (a) around 1943 (b) 1960; 4200
(c) no; you need the year’s population (d) war; marketing techniques
(e) news of health risk; social pressure, antismoking campaigns, increased taxation
2. (a) 1989; $35,600 (b) 1975, 1983; $32,000
(c) the first two years; the curve is steeper (downhill)
3. (a) −2.9, −2.0, 2.35, 2.9 (b) none (c) y = 0
(d) −1.75 ≤ x ≤ 2.15 (e) ymax = 2.8 at x = −2.6; ymin = −2.2 at x = 1.2
4. (a) x = −1, 4 (b) none (c) y = −1
(d) x = 0, 3, 5 (e) ymax = 9 at x = 6; ymin = −2 at x = 0
5. (a) x = 2, 4 (b) none (c) x ≤ 2; 4 ≤ x (d) ymin = −1; no maximum value
6. (a) x = 9 (b) none (c) x ≥ 25 (d) ymin = 1; no maximum value
7. (a) Breaks could be caused by war, pestilence, flood, earthquakes, for example.
(b) C decreases for eight hours, takes a jump upwards, and then repeats.
8. (a) Yes, if the thermometer is not near a window or door or other source of sudden temperature
change.
(b) No; the number is always an integer, so the changes are in movements (jumps) of at least
one unit.
9. (a) The side adjacent to the building has length x, so L = x + 2y. Since A = xy = 1000,
L = x + 2000/x.
(b) x > 0 and x must be smaller than the width of the building, which was not given.
(c) 120 (d) Lmin ≈ 89.44 ft
20 80
80
10. (a) V = lwh = (6 − 2x)(6 − 2x)x (b) From the figure it is clear that 0 < x < 3.
(c) 20 (d) Vmax ≈ 16 in3
0 3
0
1
Prepared by
Neil Wigley
University of Windsor
Albert Herr
To Accompany
CALCULUS
EARLY TRANSCENDENTALS
Seventh Edition
Howard Anton
Drexel University
Irl C. Bivens
Davidson College
Stephen L. Davis
Davidson College
John Wiley & Sons, Inc.
,Cover Design: Norm Christensen
To order books or for customer service call 1-800-CALL-WILEY (225-5945).
Copyright 2002 by John Wiley & Sons, Inc.
Excerpts from this work may be reproduced by instructors for
distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for
which the textbook has been adopted. Any other
reproduction or translation of this work beyond that
permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner
is unlawful. Requests for permission or further information
should be addressed to the Permissions Department, John
Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-
0012.
ISBN 0-471-43497-3
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
Printed and bound by Victor Graphics, Inc.
, CONTENTS
Chapter 1. Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 2. Limits and Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Chapter 3. The Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70
Chapter 4. Exponential, Logarithmic, and Inverse Trigonometric Functions . . . 122
Chapter 5. The Derivative in Graphing and Applications . . . . . . . . . . . . . . . . . . . . 150
Chapter 6. Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Chapter 7. Applications of the Definite Integral in Geometry,
Science, and Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .278
Chapter 8. Principles of Integral Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
Chapter 9. Mathematical Modeling with Differential Equations . . . . . . . . . . . . . . 372
Chapter 10. Infinite Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
Chapter 11. Analytic Geometry in Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .447
Chapter 12. Three-Dimensional Space; Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492
Chapter 13. Vector-Valued Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
Chapter 14. Partial Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569
Chapter 15. Multiple Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620
Chapter 16. Topics in Vector Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657
Appendix A. Real Numbers, Intervals, and Inequalities . . . . . . . . . . . . . . . . . . . . . . . 690
Appendix B. Absolute Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697
Appendix C. Coordinate Planes and Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700
Appendix D. Distance, Circles, and Quadratic Equations . . . . . . . . . . . . . . . . . . . . . . 709
Appendix E. Trigonometry Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719
Appendix F. Solving Polynomial Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725
, CHAPTER 1
Functions
EXERCISE SET 1.1
1. (a) around 1943 (b) 1960; 4200
(c) no; you need the year’s population (d) war; marketing techniques
(e) news of health risk; social pressure, antismoking campaigns, increased taxation
2. (a) 1989; $35,600 (b) 1975, 1983; $32,000
(c) the first two years; the curve is steeper (downhill)
3. (a) −2.9, −2.0, 2.35, 2.9 (b) none (c) y = 0
(d) −1.75 ≤ x ≤ 2.15 (e) ymax = 2.8 at x = −2.6; ymin = −2.2 at x = 1.2
4. (a) x = −1, 4 (b) none (c) y = −1
(d) x = 0, 3, 5 (e) ymax = 9 at x = 6; ymin = −2 at x = 0
5. (a) x = 2, 4 (b) none (c) x ≤ 2; 4 ≤ x (d) ymin = −1; no maximum value
6. (a) x = 9 (b) none (c) x ≥ 25 (d) ymin = 1; no maximum value
7. (a) Breaks could be caused by war, pestilence, flood, earthquakes, for example.
(b) C decreases for eight hours, takes a jump upwards, and then repeats.
8. (a) Yes, if the thermometer is not near a window or door or other source of sudden temperature
change.
(b) No; the number is always an integer, so the changes are in movements (jumps) of at least
one unit.
9. (a) The side adjacent to the building has length x, so L = x + 2y. Since A = xy = 1000,
L = x + 2000/x.
(b) x > 0 and x must be smaller than the width of the building, which was not given.
(c) 120 (d) Lmin ≈ 89.44 ft
20 80
80
10. (a) V = lwh = (6 − 2x)(6 − 2x)x (b) From the figure it is clear that 0 < x < 3.
(c) 20 (d) Vmax ≈ 16 in3
0 3
0
1
