E-Book Overview
Students and math professors looking for a calculus resource that sparks curiosity and engages them will appreciate this new book. Through demonstration and exercises, it shows them how to read equations. It uses a blend of traditional and reform emphases to develop intuition. Narrative and exercises present calculus as a single, unified subject. Color is used to help them identify and interpret the parts of a mathematical model. In addition, formal proofs are preceded with informal discussions that focus on the ideas about to be presented. Then the proofs are discussed in a way that helps scientists and engineers interpret the details of the argument.
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This page intentionally left blank P R E L I M I N A RY E D I T I O N CALCULUS SINGLE VARIABLE CARL V. LUTZER • H.T. GOODWILL John Wiley & Sons, Inc VICE PRESIDENT & PUBLISHER Laurie Rosatone ACQUISITIONS EDITOR David Dietz MARKETING MANAGER Jonathan Cottrell SENIOR DEVELOPMENT EDITOR Mary O’Sullivan PROJECT EDITOR Jennifer Brady SENIOR DESIGNER Jim O’Shea MEDIA EDITOR Melissa Edwards PRODUCTION MANAGER Micheline Frederick SENIOR PRODUCTION EDITOR Ken Santor This book was set in LaTex by the authors and printed and bound by Courier Kendallville. The cover was printed by Courier Kendallville. This book is printed on acid free paper. Copyright © 2011 John Wiley & Sons, Inc. 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, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc. 222 Rosewood Drive, Danvers, MA 01923, website www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201)748-6011, fax (201)7486008, website http//www.wiley.com/go/permissions. “Evaluation copies are provided to qualified academics and professionals for review purposes only, for use in their courses during the next academic year. These copies are licensed and may not be sold or transferred to a third party. Upon completion of the review period, please return the evaluation copy to Wiley. Return instructions and a free of charge return shipping label are available at www.wiley.com/go/returnlabel. Outside of the United States, please contact your local representative.” Library of Congress Cataloging in Publication Data: ISBN 13 978-0470-17930-7 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 CONTENTS Chapter 1. Tools of the Trade 1 1.1. Power Functions 1 1.2. Polynomials 10 1.3. Rational Functions 18 1.4. Algebraic, Composite, and Piecewise Functions 26 1.5. Periodic Functions & Transformations 32 1.6. Exponential Functions 48 1.7. Logarithms 57 1.8. Inverse Functions 68 • Chapter Review 76 • Projects & Applications – Richardson’s Arms Race 83 Chapter 2. Limits and Continuity 89 2.1. Introduction to Limits 89 2.2. Calculating Limits 97 2.3. Limits at Infinity 107 2.4. The Technical Definition of a Limit 116 2.5. Continuity 129 • Chapter Review 140 • Projects & Applications – The Apothem and Limits at Infinity; Implementing the Bisection Algorithm 144 Chapter 3. The Derivative 147 3.1. The Derivative 148 3.2. Derivatives of Power Functions 160 3.3. Derivatives of Trigonometric and Exponential Functions 169 3.4. The Derivative as a Function 180 3.5. The Product Ru