文档介绍：This page intentionally left blank
Student’s Solutions Manual
to pany Jon Rogawski’s
Multivariable
CALCULUS
SECOND EDITION
GREGORY P. DRESDEN
Washington and Lee University
JENNIFER BOWEN
The College of Wooster
RANDALL PAUL
Oregon Institute of Technology
W. H. FREEMAN PANY
NEW YORK
© 2012 by W. H. Freeman pany
ISBN-13: 978-1-4292-5508-0
ISBN-10: 1-4292-5508-0
All rights reserved
Printed in the United States of America
First Printing
W. H. Freeman pany, 41 Madison Avenue, New York, NY 10010
Houndmills, Basingstoke RG21 6XS, England
CONTENTS
Chapter 10 INFINITE SERIES (LT Chapter 11) 1 Chapter 14 DIFFERENTIATION IN SEVERAL
VARIABLES (LT Chapter 15) 336
Sequences (LT Section ) 1
Summing an Infinite Series (LT Section ) 13 Functions of Two or More Variables
Convergence of Series with Positive Terms (LT Section ) 336
(LT Section ) 23 Limits and Continuity in Several Variables
Absolute and Conditional Convergence (LT Section ) 345
(LT Section ) 38 Partial Derivatives (LT Section ) 351
The Ratio and Root Tests (LT Section ) 44 Differentiability and Tangent Planes
Power Series (LT Section ) 52 (LT Section ) 363
Taylor Series (LT Section ) 64 The Gradient and Directional Derivatives
Chapter Review Exercises 81 (LT Section ) 374
The Chain Rule (LT Section ) 386
Optimization in Several Variables
Chapter 11 PARAMETRIC EQUATIONS, (LT Section ) 399
POLAR COORDINATES, Lagrange Multipliers: Optimizing with a Constraint
AND CONIC SECTIONS (LT Section ) 419
(LT Chapter 12) 96 Chapter Review Exercises 442
Parametric Equations (LT Section ) 96 Chapter 15 MULTIPLE INTEGRATION
Arc Length and Speed (LT Section ) 112 (LT Chapter 16) 458
Polar Coordinates (LT Section ) 120
Area and Arc Length in Polar Coordinates
Integration in Two Variables (LT Section 1