, SCHAUM'S
OUTLINE OF
3000 SOLVED
PROBLEMS IN
Calculus
Elliot Mendelson, Ph.D.
Professor of Mathematics
Queens College
City University of New York
Schaum's Outline Series
MC
Graw
Hill
New York Chicago San Francisco Lisbon
London Madrid Mexico City Milan New Delhi
San Juan Seoul Singapore Sydney Toronto
,Copyright © 1988 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part
of 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 written
permission of the publisher.
ISBN: 978-0-07-170261-4
MHID: 0-07-170261-X
The 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. Rather than put a trademark symbol after every occurrence of a trademarked name, we use
names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designa-
tions 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. To
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TERMS OF USE
This is a copyrighted work and The McGraw-Hill Companies, Inc. (“McGrawHill”) and its licensors reserve all rights in and to the work. Use of this
work is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may
not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate, sell, publish or
sublicense the work or any part of it without McGraw-Hill’s prior consent. You may use the work for your own noncommercial and personal use; any
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THE WORK IS PROVIDED “AS IS.” McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE AC-
CURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFOR-
MATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WAR-
RANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS
FOR A PARTICULAR PURPOSE. McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet your
requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any
inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has no responsibility for the content
of any information accessed through the work. 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 the
possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort
or otherwise.
, CONTENTS
Chapter 1 INEQUALITIES 1
Chapter 2 ABSOLUTE VALUE 5
Chapter 3 LINES 9
Chapter 4 CIRCLES 19
Chapter 5 FUNCTIONS AND THEIR GRAPHS 23
Chapter 6 LIMITS 35
Chapter 7 CONTINUITY 43
Chapter 8 THE DERIVATIVE 49
Chapter 9 THE CHAIN RULE 56
Chapter 10 TRIGONOMETRIC FUNCTIONS AND THEIR DERIVATIVES 62
Chapter 11 ROLLE'S THEOREM, THE MEAN VALUE THEOREM, AND THE SIGN
OF THE DERIVATIVE 69
Chapter 12 HIGHER-ORDER DERIVATIVES AND IMPLICIT DIFFERENTIATION 75
Chapter 13 MAXIMA AND MINIMA 81
Chapter 14 RELATED RATES 88
Chapter 15 CURVE SKETCHING (GRAPHS) 100
Chapter 16 APPLIED MAXIMUM AND MINIMUM PROBLEMS 118
Chapter 17 RECTILINEAR MOTION 133
Chapter 18 APPROXIMATION BY DIFFERENTIALS 138
Chapter 19 ANTIDERIVATIVES (INDEFINITE INTEGRALS) 142
Chapter 20 THE DEFINITE INTEGRAL AND THE FUNDAMENTAL THEOREM OF
CALCULUS 152
Chapter 21 AREA AND ARC LENGTH 163
Chapter 22 VOLUME 173
Chapter 23 THE NATURAL LOGARITHM 185
Chapter 24 EXPONENTIAL FUNCTIONS 195
Chapter 25 L'HOPITAL'S RULE 208
Chapter 26 EXPONENTIAL GROWTH AND DECAY 215
iii
OUTLINE OF
3000 SOLVED
PROBLEMS IN
Calculus
Elliot Mendelson, Ph.D.
Professor of Mathematics
Queens College
City University of New York
Schaum's Outline Series
MC
Graw
Hill
New York Chicago San Francisco Lisbon
London Madrid Mexico City Milan New Delhi
San Juan Seoul Singapore Sydney Toronto
,Copyright © 1988 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part
of 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 written
permission of the publisher.
ISBN: 978-0-07-170261-4
MHID: 0-07-170261-X
The 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. Rather than put a trademark symbol after every occurrence of a trademarked name, we use
names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designa-
tions 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. To
contact a representative please e-mail us at .
TERMS OF USE
This is a copyrighted work and The McGraw-Hill Companies, Inc. (“McGrawHill”) and its licensors reserve all rights in and to the work. Use of this
work is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may
not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate, sell, publish or
sublicense the work or any part of it without McGraw-Hill’s prior consent. You may use the work for your own noncommercial and personal use; any
other use of the work is strictly prohibited. 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 AC-
CURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFOR-
MATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WAR-
RANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS
FOR A PARTICULAR PURPOSE. McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet your
requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any
inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has no responsibility for the content
of any information accessed through the work. 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 the
possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort
or otherwise.
, CONTENTS
Chapter 1 INEQUALITIES 1
Chapter 2 ABSOLUTE VALUE 5
Chapter 3 LINES 9
Chapter 4 CIRCLES 19
Chapter 5 FUNCTIONS AND THEIR GRAPHS 23
Chapter 6 LIMITS 35
Chapter 7 CONTINUITY 43
Chapter 8 THE DERIVATIVE 49
Chapter 9 THE CHAIN RULE 56
Chapter 10 TRIGONOMETRIC FUNCTIONS AND THEIR DERIVATIVES 62
Chapter 11 ROLLE'S THEOREM, THE MEAN VALUE THEOREM, AND THE SIGN
OF THE DERIVATIVE 69
Chapter 12 HIGHER-ORDER DERIVATIVES AND IMPLICIT DIFFERENTIATION 75
Chapter 13 MAXIMA AND MINIMA 81
Chapter 14 RELATED RATES 88
Chapter 15 CURVE SKETCHING (GRAPHS) 100
Chapter 16 APPLIED MAXIMUM AND MINIMUM PROBLEMS 118
Chapter 17 RECTILINEAR MOTION 133
Chapter 18 APPROXIMATION BY DIFFERENTIALS 138
Chapter 19 ANTIDERIVATIVES (INDEFINITE INTEGRALS) 142
Chapter 20 THE DEFINITE INTEGRAL AND THE FUNDAMENTAL THEOREM OF
CALCULUS 152
Chapter 21 AREA AND ARC LENGTH 163
Chapter 22 VOLUME 173
Chapter 23 THE NATURAL LOGARITHM 185
Chapter 24 EXPONENTIAL FUNCTIONS 195
Chapter 25 L'HOPITAL'S RULE 208
Chapter 26 EXPONENTIAL GROWTH AND DECAY 215
iii
