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Complete Solutions Manual
for
MULTIVARIABLE CALCULUS
SEVENTH EDITION
DAN CLEGG
Palomar College
BARBARA FRANK
Cape Fear Community College
Australia . Brazil . Japan . Korea . Mexico . Singapore . Spain . United Kingdom . United States
© Cengage Learning.
g.. All
A Rights Reserved.
, Free ebooks ==> www.ebook777.com
© 2012 Brooks/Cole, Cengage Learning ISBN-13: 978-0-8400-4947-6
ISBN-10: 0-8400-4947-1
ALL RIGHTS RESERVED. No part of this work covered by the
copyright herein may be reproduced, transmitted, stored, or Brooks/Cole
used in any form or by any means graphic, electronic, or 20 Davis Drive
mechanical, including but not limited to photocopying, Belmont, CA 94002-3098
recording, scanning, digitizing, taping, Web distribution, USA
information networks, or information storage and retrieval
systems, except as permitted under Section 107 or 108 of the Cengage Learning is a leading provider of customized
1976 United States Copyright Act, without the prior written learning solutions with office locations around the globe,
permission of the publisher except as may be permitted by including Singapore, the United Kingdom, Australia,
the license terms below. Mexico, Brazil, and Japan. Locate your local office at:
www.cengage.com/global
Cengage Learning products are represented in
For product information and technology assistance, contact us at Canada by Nelson Education, Ltd.
Cengage Learning Customer & Sales Support,
1-800-354-9706 To learn more about Brooks/Cole, visit
www.cengage.com/brookscole
For permission to use material from this text or product,
submit all requests online at www.cengage.com/permissions Purchase any of our products at our preferred online store
Further permissions questions can be e-mailed to www.cengagebrain.com
NOTE: UNDER NO CIRCUMSTANCES MAY THIS MATERIAL OR ANY PORTION THEREOF BE SOLD, LICENSED, AUCTIONED,
OR OTHERWISE REDISTRIBUTED EXCEPT AS MAY BE PERMITTED BY THE LICENSE TERMS HEREIN.
READ IMPORTANT LICENSE INFORMATION
Dear Professor or Other Supplement Recipient: material posted electronically must be through a password-
protected site, with all copy and download functionality disabled,
Cengage Learning has provided you with this product (the and accessible solely by your students who have purchased the
“Supplement”) for your review and, to the extent that you adopt associated textbook for the Course. You may not sell, license,
the associated textbook for use in connection with your course auction, or otherwise redistribute the Supplement in any form. We
(the “Course”), you and your students who purchase the ask that you take reasonable steps to protect the Supplement from
textbook may use the Supplement as described below. unauthorized use, reproduction, or distribution. Your use of the
Cengage Learning has established these use limitations in Supplement indicates your acceptance of the conditions set forth in
response to concerns raised by authors, professors, and other this Agreement. If you do not accept these conditions, you must
users regarding the pedagogical problems stemming from return the Supplement unused within 30 days of receipt.
unlimited distribution of Supplements.
All rights (including without limitation, copyrights, patents, and trade
Cengage Learning hereby grants you a nontransferable license secrets) in the Supplement are and will remain the sole and
to use the Supplement in connection with the Course, subject to exclusive property of Cengage Learning and/or its licensors. The
the following conditions. The Supplement is for your personal, Supplement is furnished by Cengage Learning on an “as is” basis
noncommercial use only and may not be reproduced, or without any warranties, express or implied. This Agreement will be
distributed, except that portions of the Supplement may be governed by and construed pursuant to the laws of the State of
provided to your students in connection with your instruction of New York, without regard to such State’s conflict of law rules.
the Course, so long as such students are advised that they may
not copy or distribute any portion of the Supplement to any third Thank you for your assistance in helping to safeguard the integrity
party. Test banks, and other testing materials may be made of the content contained in this Supplement. We trust you find the
available in the classroom and collected at the end of each class Supplement a useful teaching tool.
session, or posted electronically as described herein. Any
Printed in the United States of America
1 2 3 4 5 6 7 15 14 1 3 1 2 11
www.ebook777.com
© Cengage Learning.
g.. All
A Rights Reserved.
, Free ebooks ==> www.ebook777.com
■ PREFACE
This Complete Solutions Manual contains detailed solutions to all exercises in the text Multivariable
Calculus, Seventh Edition (Chapters 10–17 of Calculus, Seventh Edition, and Calculus: Early
Transcendentals, Seventh Edition) by James Stewart. A Student Solutions Manual is also available,
which contains solutions to the odd-numbered exercises in each chapter section, review section,
True-False Quiz, and Problems Plus section as well as all solutions to the Concept Check questions.
(It does not, however, include solutions to any of the projects.)
Because of differences between the regular version and the Early Transcendentals version of the
text, some references are given in a dual format. In these cases, users of the Early Transcendentals
text should use the references denoted by “ET.”
While we have extended every effort to ensure the accuracy of the solutions presented, we would
appreciate correspondence regarding any errors that may exist. Other suggestions or comments are
also welcome, and can be sent to dan clegg at or in care of the publisher:
Brooks/Cole, Cengage Learning, 20 Davis Drive, Belmont CA 94002-3098.
We would like to thank James Stewart for entrusting us with the writing of this manual and offer-
ing suggestions and Kathi Townes of TECH-arts for typesetting and producing this manual as well as
creating the illustrations. We also thank Richard Stratton, Liz Covello, and Elizabeth Neustaetter of
Brooks/Cole, Cengage Learning, for their trust, assistance, and patience.
DAN CLEGG
Palomar College
BARBARA FRANK
Cape Fear Community College
© Cengage Learning.
g.. All
A Rights Reserved.
www.ebook777.com
,Free ebooks ==> www.ebook777.com
Complete Solutions Manual
for
MULTIVARIABLE CALCULUS
SEVENTH EDITION
DAN CLEGG
Palomar College
BARBARA FRANK
Cape Fear Community College
Australia . Brazil . Japan . Korea . Mexico . Singapore . Spain . United Kingdom . United States
© Cengage Learning.
g.. All
A Rights Reserved.
, Free ebooks ==> www.ebook777.com
© 2012 Brooks/Cole, Cengage Learning ISBN-13: 978-0-8400-4947-6
ISBN-10: 0-8400-4947-1
ALL RIGHTS RESERVED. No part of this work covered by the
copyright herein may be reproduced, transmitted, stored, or Brooks/Cole
used in any form or by any means graphic, electronic, or 20 Davis Drive
mechanical, including but not limited to photocopying, Belmont, CA 94002-3098
recording, scanning, digitizing, taping, Web distribution, USA
information networks, or information storage and retrieval
systems, except as permitted under Section 107 or 108 of the Cengage Learning is a leading provider of customized
1976 United States Copyright Act, without the prior written learning solutions with office locations around the globe,
permission of the publisher except as may be permitted by including Singapore, the United Kingdom, Australia,
the license terms below. Mexico, Brazil, and Japan. Locate your local office at:
www.cengage.com/global
Cengage Learning products are represented in
For product information and technology assistance, contact us at Canada by Nelson Education, Ltd.
Cengage Learning Customer & Sales Support,
1-800-354-9706 To learn more about Brooks/Cole, visit
www.cengage.com/brookscole
For permission to use material from this text or product,
submit all requests online at www.cengage.com/permissions Purchase any of our products at our preferred online store
Further permissions questions can be e-mailed to www.cengagebrain.com
NOTE: UNDER NO CIRCUMSTANCES MAY THIS MATERIAL OR ANY PORTION THEREOF BE SOLD, LICENSED, AUCTIONED,
OR OTHERWISE REDISTRIBUTED EXCEPT AS MAY BE PERMITTED BY THE LICENSE TERMS HEREIN.
READ IMPORTANT LICENSE INFORMATION
Dear Professor or Other Supplement Recipient: material posted electronically must be through a password-
protected site, with all copy and download functionality disabled,
Cengage Learning has provided you with this product (the and accessible solely by your students who have purchased the
“Supplement”) for your review and, to the extent that you adopt associated textbook for the Course. You may not sell, license,
the associated textbook for use in connection with your course auction, or otherwise redistribute the Supplement in any form. We
(the “Course”), you and your students who purchase the ask that you take reasonable steps to protect the Supplement from
textbook may use the Supplement as described below. unauthorized use, reproduction, or distribution. Your use of the
Cengage Learning has established these use limitations in Supplement indicates your acceptance of the conditions set forth in
response to concerns raised by authors, professors, and other this Agreement. If you do not accept these conditions, you must
users regarding the pedagogical problems stemming from return the Supplement unused within 30 days of receipt.
unlimited distribution of Supplements.
All rights (including without limitation, copyrights, patents, and trade
Cengage Learning hereby grants you a nontransferable license secrets) in the Supplement are and will remain the sole and
to use the Supplement in connection with the Course, subject to exclusive property of Cengage Learning and/or its licensors. The
the following conditions. The Supplement is for your personal, Supplement is furnished by Cengage Learning on an “as is” basis
noncommercial use only and may not be reproduced, or without any warranties, express or implied. This Agreement will be
distributed, except that portions of the Supplement may be governed by and construed pursuant to the laws of the State of
provided to your students in connection with your instruction of New York, without regard to such State’s conflict of law rules.
the Course, so long as such students are advised that they may
not copy or distribute any portion of the Supplement to any third Thank you for your assistance in helping to safeguard the integrity
party. Test banks, and other testing materials may be made of the content contained in this Supplement. We trust you find the
available in the classroom and collected at the end of each class Supplement a useful teaching tool.
session, or posted electronically as described herein. Any
Printed in the United States of America
1 2 3 4 5 6 7 15 14 1 3 1 2 11
www.ebook777.com
© Cengage Learning.
g.. All
A Rights Reserved.
, Free ebooks ==> www.ebook777.com
■ PREFACE
This Complete Solutions Manual contains detailed solutions to all exercises in the text Multivariable
Calculus, Seventh Edition (Chapters 10–17 of Calculus, Seventh Edition, and Calculus: Early
Transcendentals, Seventh Edition) by James Stewart. A Student Solutions Manual is also available,
which contains solutions to the odd-numbered exercises in each chapter section, review section,
True-False Quiz, and Problems Plus section as well as all solutions to the Concept Check questions.
(It does not, however, include solutions to any of the projects.)
Because of differences between the regular version and the Early Transcendentals version of the
text, some references are given in a dual format. In these cases, users of the Early Transcendentals
text should use the references denoted by “ET.”
While we have extended every effort to ensure the accuracy of the solutions presented, we would
appreciate correspondence regarding any errors that may exist. Other suggestions or comments are
also welcome, and can be sent to dan clegg at or in care of the publisher:
Brooks/Cole, Cengage Learning, 20 Davis Drive, Belmont CA 94002-3098.
We would like to thank James Stewart for entrusting us with the writing of this manual and offer-
ing suggestions and Kathi Townes of TECH-arts for typesetting and producing this manual as well as
creating the illustrations. We also thank Richard Stratton, Liz Covello, and Elizabeth Neustaetter of
Brooks/Cole, Cengage Learning, for their trust, assistance, and patience.
DAN CLEGG
Palomar College
BARBARA FRANK
Cape Fear Community College
© Cengage Learning.
g.. All
A Rights Reserved.
