This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tortor otherwise.ĬONTENTSChapter 1INEQUALITIES1Chapter 2ABSOLUTE VALUE5Chapter 3LINES9Chapter 4CIRCLES19Chapter 5FUNCTIONS AND THEIR GRAPHS23Chapter 6LIMITS35Chapter 7CONTINUITY43Chapter 8THE DERIVATIVE49Chapter 9THE CHAIN RULE56Chapter 10TRIGONOMETRIC FUNCTIONS AND THEIR DERIVATIVES62Chapter 11ROLLE'S THEOREM, THE MEAN VALUE THEOREM, AND THE SIGNOF THE DERIVATIVE69Chapter 12HIGHER-ORDER DERIVATIVES AND IMPLICIT DIFFERENTIATION75Chapter 13MAXIMA AND MINIMA81Chapter 14RELATED RATES88Chapter 15CURVE SKETCHING (GRAPHS)100Chapter 16APPLIED MAXIMUM AND MINIMUM PROBLEMS118Chapter 17RECTILINEAR MOTION133Chapter 18APPROXIMATION BY DIFFERENTIALS138Chapter 19ANTIDERIVATIVES (INDEFINITE INTEGRALS)142Chapter 20THE DEFINITE INTEGRAL AND THE FUNDAMENTAL THEOREM OFCALCULUS152Chapter 21AREA AND ARC LENGTH163Chapter 22VOLUME173Chapter 23THE NATURAL LOGARITHM185Chapter 24EXPONENTIAL FUNCTIONS195Chapter 25L'HOPITAL'S RULE208Chapter 26EXPONENTIAL GROWTH AND DECAY215iii Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental,special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of thepossibility of such damages. McGraw-Hill has no responsibility for the contentof any information accessed through the work. Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for anyinaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet yourrequirements or that its operation will be uninterrupted or error free. Your right to use the work may be terminated if you fail to comply with these terms.THE WORK IS PROVIDED “AS IS.” McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESSFOR A PARTICULAR PURPOSE. You may use the work for your own noncommercial and personal use anyother use of the work is strictly prohibited. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you maynot decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate, sell, publish orsublicense the work or any part of it without McGraw-Hill’s prior consent. Use of thiswork is subject to these terms. (“McGrawHill”) and its licensors reserve all rights in and to the work. Tocontact a representative please e-mail us at OF USEThis is a copyrighted work and The McGraw-Hill Companies, Inc. Where such designations appear in this book, they have been printed with initial caps.McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs. Rather than put a trademark symbol after every occurrence of a trademarked name, we usenames in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Except as permitted under the United States Copyright Act of 1976, no partof this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior writtenpermission of the publisher.ISBN: 978-0-07-170261-4MHID: 0-07-170261-XThe material in this eBook also appears in the print version of this title: ISBN: 978-0-07-163534-9,MHID: 0-07-163534-3.All trademarks are trademarks of their respective owners. SCHAUM'SOUTLINE OF3000 SOLVEDPROBLEMS INCalculusElliot Mendelson, Ph.D.Professor of MathematicsQueens CollegeCity University of New YorkSchaum's Outline SeriesMCGrawHillNew York Chicago San Francisco LisbonLondon Madrid Mexico City Milan New DelhiSan Juan Seoul Singapore Sydney TorontoĬopyright 1988 by The McGraw-Hill Companies, Inc.