INSTRUCTOR’S
S
OLUTIONS MANUAL
MULTIVARIABLE
WILLIAM ARDIS
Collin County Community College
THOMAS’ CALCULUS
TWELFTH EDITION
BASED ON THE ORIGINAL WORK BY
George B. Thomas, Jr.
Massachusetts Institute of Technology
AS REVISED BY
Maurice D. Weir
Naval Postgraduate School
Joel Hass
University of California, Davis
The author and publisher of this book have used their best efforts in preparing this book. These efforts
include the development, research, and testing of the theories and programs to determine their
effectiveness. The author and publisher make no warranty of any kind, expressed or implied, with regard to
these programs or the documentation contained in this book. The author and publisher shall not be liable in
any event for incidental or consequential damages in connection with, or arising out of, the furnishing,
performance, or use of these programs.
Reproduced by Addison-Wesley from electronic files supplied by the author.
Copyright © 2010, 2005, 2001 Pearson Education, Inc.
Publishing as Pearson Addison-Wesley, 75 Arlington Street, Boston, MA 02116.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or
transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise,
without the prior written permission of the publisher. Printed in the United States of America.
ISBN-13: 978-0-321-60072-1
ISBN-10: 0-321-60072-X
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PREFACE TO THE INSTRUCTOR
This Instructor's Solutions Manual contains the solutions to every exercise in the 12th Edition of THOMAS' CALCULUS
by Maurice Weir and Joel Hass, including the Computer Algebra System (CAS) exercises. The corresponding Student's
Solutions Manual omits the solutions to the even-numbered exercises as well as the solutions to the CAS exercises (because
the CAS command templates would give them all away).
In addition to including the solutions to all of the new exercises in this edition of Thomas, we have carefully revised or
rewritten every solution which appeared in previous solutions manuals to ensure that each solution
conforms exactly to the methods, procedures and steps presented in the textì
is mathematically correctì
includes all of the steps necessary so a typical calculus student can follow the logical argument and algebraì
includes a graph or figure whenever called for by the exercise, or if needed to help with the explanationì
is formatted in an appropriate style to aid in its understandingì
Every CAS exercise is solved in both the MAPLE and computer algebra systems. A template showingMATHEMATICA
an example of the CAS commands needed to execute the solution is provided for each exercise type. Similar exercises within
the text grouping require a change only in the input function or other numerical input parameters associated with the problem
(such as the interval endpoints or the number of iterations).
For more information about other resources available with Thomas' Calculus, visit http://pearsonhighered.com.
Copyright © 2010 Pearson Education Inc. Publishing as Addison-Wesley.
TABLE OF CONTENTS
10 Infinite Sequences and Series 569
10.1 Sequences 569
10.2 Infinite Series 577
10.3 The Integral Test 583
10.4 Comparison Tests 590
10.5 The Ratio and Root Tests 597
10.6 Alternating Series, Absolute and Conditional Convergence 602
10.7 Power Series 608
10.8 Taylor and Maclaurin Series 617
10.9 Convergence of Taylor Series 621
10.10 The Binomial Series and Applications of Taylor Series 627
Practice Exercises 634
Additional and Advanced Exercises 642
11 Parametric Equations and Polar Coordinates 647
11.1 Parametrizations of Plane Curves 647
11.2 Calculus with Parametric Curves 654
11.3 Polar Coordinates 662
11.4 Graphing in Polar Coordinates 667
11.5 Areas and Lengths in Polar Coordinates 674
11.6 Conic Sections 679
11.7 Conics in Polar Coordinates 689
Practice Exercises 699
Additional and Advanced Exercises 709
12 Vectors and the Geometry of Space 715
12.1 Three-Dimensional Coordinate Systems 715
12.2 Vectors 718
12.3 The Dot Product 723
12.4 The Cross Product 728
12.5 Lines and Planes in Space 734
12.6 Cylinders and Quadric Surfaces 741
Practice Exercises 746
Additional Exercises 754
13 Vector-Valued Functions and Motion in Space 759
13.1 Curves in Space and Their Tangents 759
13.2 Integrals of Vector Functions; Projectile Motion 764
13.3 Arc Length in Space 770
13.4 Curvature and Normal Vectors of a Curve 773
13.5 Tangential and Normal Components of Acceleration 778
13.6 Velocity and Acceleration in Polar Coordinates 784
Practice Exercises 785
Additional Exercises 791
Copyright © 2010 Pearson Education Inc. Publishing as Addison-Wesley.
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