with analytk: geometry
Earl W Swokowski
Prindle, Weber & Schmidt
Dedicated to the memory of my mother and father; Sophia and john Swokowski
Pnndle Weber & Schmrdt ·II.'· Wollard Granl Press · ooc: · Duxbury Press · • Statler Off1ce Bu•ld.ng · 20 Prov•dence Street · BostonMassachusetts 02116
Copyright© 1983 by PWS Publishers All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission, in writing, from the publisher.
PWS Publishers is a division of Wadsworth, Inc.
Portions of this bookpreviously appeared in Calculus with Analytic Geometry, Second Edition by Earl W. Swokowski. Copyright © 1979 by Prindle, Weber & Schmidt. 87 86 85 84 83 10 9 8 7 6 5 4 3 2
Library of Congress Cataloging in Publication Data
Swokowski, Earl W. Calculus with analytic geometry. Includes index. I. Calculus. 2. Geometry, Analytic. 515'.15 82-21481 QA303.S94 1983 ISBN 0-87150-341-7I. Title
Cover image courtesy of General Motors Research Laboratories. The computer graphic image depicts the location of valence electrons trapped near the surface of rhodium. Quantum mechanical calculations using the Schrodingerequation were employed to generate the image. The two sets of peaks in the foreground reveal a preferential accumulation of electrons around the surface atoms.Production and design: Kathi Townes Text composition: Composition House Limited Technical artwork: Vantage Art, Inc. Cover printing: Federated Lithographers-Printers, Inc. Text printing/binding: Von Hoffmann Press, Inc.
Printed in the United States of America
Most students study calculus for its use as a tool in areas other than mathematics. They desire information about why calculus isimportant, and where and how it can be applied. I kept these facts in mind as I wrote this text. In particular, when introducing new concepts I often refer to problems that are familiar to students and that require methods of calculus for solutions. Numerous examples and exercises have been designed to further motivate student interest, not only in the mathematical or physical sciences, but inother disciplines as well. Figures are frequently used to bridge the gap between the statement of a problem and its solution. In addition to achieving a good balance between theory -and applications, my primary objective was to write a book that can be read and understood by college freshmen. In each section I have striven for accuracy and clarity of exposition, together with a presentation thatmakes the transition from precalculus mathematics to calculus as smooth as possible. The comments that follow highlight some of the features of this text. A review of the trigonometric functions is contained in the last section of Chapter I. It was placed there, instead of in an appendix, to alert students to the fact that trigonometry is, indeed, a prerequisite for calculus, as indicated by thetitle of the chapter. Tests for symmetry are also introduced early, so that they can be used throughout the text. In Chapter 2 limits involving the sine and cosine functions are considered after limits of algebraic functions, and thus are readily available for use in obtaining derivative formulas in Chapter 3. The early introduction of trigonometric
functions leads to some nontrivial applicationsof the Chain Rule and enlarges the scope of applications of the derivative. In Chapter4testvalues are used to determine intervals in which derivatives are positive or negative. This pedagogical device is also employed to help obtain graphs of rational functions. Chapters 5 and 6, on properties and applications of definite integrals, include exercises on numerical integration that require...