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Single Variable Calculus Early Transcendentals, 9th Edition, Metric Edition by Stewart, James, Clegg, Daniel K., Watson, Saleem, Redlin, Lothar (2020) Single Variable Calculus Early Transcendentals, 9th Edition, Metric Edition by Stewart, James, Clegg, Daniel K., Watson, Saleem, Redlin, Lothar (2020) Single Variable Calculus Early Transcendentals, 9th Edition, Metric Edition by Stewart, James, Clegg, Daniel K., Watson, Saleem, Redlin, Lothar (2020) Single Variable Calculus Early Transcendentals, 9th Edition, Metric Edition by Stewart, James, Clegg, Daniel K., Watson, Saleem, Redlin, Lothar (2020)
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WebAssign from Cengage can help WebAssign is an online learning platform for your math, statistics, physical sciences and engineering courses It helps you practice, focus your study time and absorb what you learn When class comes—you’re way more confide t With WebAssign you will: Get instant feedback and grading Know how well you understand concepts Watch videos and tutorials when you’re stuck Perform better on in-class assignments Ask your instructor today how you can get access to WebAssign! cengage.com/webassign Copyright 2021 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it REFERENCE page Cut here and keep for reference ALGEBRA GEOMETRY Arithmetic Operations Geometric Formulas a c ad bc − b d bd a a d ad b − − c b c bc d asb cd − ab ac a1c a c − b b b Formulas for area A, circumference C, and volume V: Triangle − 12 ab sin Exponents and Radicals a xm − x m2n xn x2n − n x x m x n − x m1n sx mdn − x m n SD n x y sxydn − x n y n n m n x myn − s x − (s x) n x 1yn − s x Î n n n s xy − s x s y n A − r A − 12 r 2 C − 2 r sx x − n y sy n V− s − r s in radiansd r r b Sphere m Sector of Circle h ¨ xn yn − Circle A − 12 bh 3 r ă s r Cylinder Cone V 13 r 2h V − r 2h A − 4 r A − rsr h r Factoring Special Polynomials r x 2 y − sx ydsx yd x y − sx ydsx 2 xy y 2d r x y − sx ydsx xy y 2d Binomial Theorem Distance and Midpoint Formulas sx yd2 − x 2xy y 2 sx yd2 − x 2 2xy y Distance between P1sx1, y1d and P2sx 2, y2d: sx yd3 − x 3x y 3xy y d − ssx 2 x1d2 s y2 y1d2 sx yd3 − x 3x y 3xy 2 y sx ydn − x n nx n21y where SD n k nsn 1d n22 x y SD n n2k k … x y 1 nxy n21 y n k nsn 1d … sn k 1d − 1?2?3?…?k … h h Midpoint of P1 P2: m− y y1 − msx x1d Slope-intercept equation of line with slope m and y-intercept b: If a , b and c 0, then ca , cb y − mx b If a , b and c , 0, then ca cb | | | | | x | a means x a or x , 2a x − a means x − a or x − 2a y2 y1 x 2 x1 Point-slope equation of line through P1sx1, y1d with slope m: If a , b and b , c, then a , c If a 0, then D Slope of line through P1sx1, y1d and P2sx 2, y2d: Inequalities and Absolute Value If a , b, then a c , b c x1 x y1 y2 , 2 Lines Quadratic Formula 2b sb 2 4ac If ax bx c − 0, then x − 2a S Circles Equation of the circle with center sh, kd and radius r: x , a means 2a , x , a sx hd2 s y kd2 − r Copyright 2021 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it REFERENCE page TRIGONOMETRY Angle Measurement Fundamental Identities csc − sin sec − cos tan − sin cos cot − cos sin s in radiansd cot − tan sin2 cos2 − Right Angle Trigonometry 1 tan2 − sec 1 cot − csc sins2 d − 2sin coss2 d − cos tans2 d − 2tan sin radians − 1808 18 − rad 180 rad r 180 ă r s r opp hyp csc − cos − adj hyp sec − hyp adj tan − opp adj cot − adj opp sin − s hyp opp hyp opp ă adj cos Trigonometric Functions sin − y r csc − x cos − r y tan − x − sin tan − cos − cot The Law of Sines y r y S D S D S D r sec − x x cot − y r B sin A sin B sin C − − a b c (x, y) a ă The Law of Cosines x b a − b c 2 2bc cos A Graphs of Trigonometric Functions y b − a c 2 2ac cos B y y=sin x π 2π y y=tan x c − a b 2 2ab cos C A y=cos x 2π x _1 C c π _1 2π x π Addition and Subtraction Formulas x sinsx yd − sin x cos y cos x sin y sinsx yd − sin x cos y cos x sin y cossx yd − cos x cos y sin x sin y y y y=csc x y=cot x cossx yd − cos x cos y sin x sin y 1 _1 y y=sec x π 2π x π _1 2π x 2π x π tansx yd − tan x tan y tan x tan y tansx yd − tan x tan y 1 tan x tan y Double-Angle Formulas sin 2x − sin x cos x Trigonometric Functions of Important Angles radians sin cos tan 08 0 s3y2 s3y3 1y2 s3 308 y6 1y2 458 y4 s2y2 608 y3 908 y2 1 — s3y2 s2y2 1 cos 2x − cos 2x sin 2x − cos 2x − 2 sin 2x tan 2x − tan x tan2x Half-Angle Formulas sin 2x − cos 2x 1 cos 2x cos 2x − 2 Copyright 2021 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it SINGLE VAR I A B LE CALCULUS EARLY TR AN S CE NDE NTA LS NINTH EDITION Met r i c Ve r si on JAMES STEWART McMASTER UNIVERSITY AND UNIVERSITY OF TORONTO DANIEL CLEGG PALOMAR COLLEGE SALEEM WATSON CALIFORNIA STATE UNIVERSITY, LONG BEACH Australia • Brazil • Mexico • Singapore • United Kingdom • United States Copyright 2021 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it This is an electronic version of the print textbook Due to electronic rights restrictions, some third party content may be suppressed Editorial review has deemed that any suppressed content does not materially affect the overall learning experience The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest Important Notice: Media content referenced within the product description or the product text may not be available in the eBook version Copyright 2021 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Single Variable Calculus: Early Transcendentals, Ninth Edition, Metric Version © 2021, 2016 Cengage Learning, Inc James Stewart, Daniel Clegg, Saleem Watson ALL RIGHTS RESERVED No part of this work covered by the copyright herein Metric Version Prepared by Anthony Tan and Michael Verwer both at McMaster University permitted by U.S copyright law, without the prior written permission of the WCN: 02-300 may be reproduced or distributed in any form or by any means, except as copyright owner International Product Director, Global Editions: For product information and technology assistance, contact us at Timothy L Anderson Cengage Customer & Sales Support, 1-800-354-9706 or support.cengage.com Product Assistant: Andrew Reddish Content Manager: Emma Collins For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions Production Service: Kathi Townes, TECHart Compositor: Graphic World Art Director: Angela Sheehan, Vernon Boes IP Analyst: Ashley Maynard ISBN: 978-0-357-11352-3 Cengage International Offices Asia Australia/New Zealand www.cengageasia.com www.cengage.com.au tel: (65) 6410 1200 tel: (61) 9685 4111 Brazil India www.cengage.com.br www.cengage.co.in Cover Designer: Nadine Ballard tel: (55) 11 3665 9900 tel: (91) 11 4364 1111 Cover Image: WichitS/ShutterStock.com Latin America UK/Europe/Middle East/Africa www.cengage.com.mx www.cengage.co.uk tel: (52) 55 1500 6000 tel: (44) 1264 332 424 IP Project Manager: Carly Belcher Manager, Global IP Integration: Eleanor Rummer Text Designer: Diane Beasley Represented in Canada by Nelson Education, Ltd tel: (416) 752 9100 / (800) 668 0671 www.nelson.com Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan Locate your local office at: www.cengage.com/global For product information: www.cengage.com/international Visit your local office: www.cengage.com/global Visit our corporate website: www.cengage.com Printed in China Print Number: 01 Print Year: 2019 Copyright 2021 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it To Lothar Redlin, our friend and colleague Copyright 2021 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Copyright 2021 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Contents Preface x A Tribute to James Stewart xxii About the Authors xxiii Technology in the Ninth Edition xxiv To the Student xxv Diagnostic Tests xxvi A Preview of Calculus Functions and Models 1.1 1.2 1.3 1.4 1.5 Four Ways to Represent a Function Mathematical Models: A Catalog of Essential Functions 21 New Functions from Old Functions 36 Exponential Functions 45 Inverse Functions and Logarithms 54 Review 67 Principles of Problem Solving 70 Limits and Derivatives 2.1 2.2 2.3 2.4 2.5 2.6 2.7 77 The Tangent and Velocity Problems 78 The Limit of a Function 83 Calculating Limits Using the Limit Laws 94 The Precise Definition of a Limit 105 Continuity 115 Limits at Infinity; Horizontal Asymptotes 127 Derivatives and Rates of Change 140 wr i t in g pr oj ec t • Early Methods for Finding Tangents 152 2.8 The Derivative as a Function 153 Review 166 Problems Plus 171 v Copyright 2021 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it ... rights restrictions require it Single Variable Calculus: Early Transcendentals, Ninth Edition, Metric Version © 2021, 2016 Cengage Learning, Inc James Stewart, Daniel Clegg, Saleem Watson ALL RIGHTS... Essential Calculus: Early Transcendentals, Second Edition, resembles Essential Calculus, but the exponential, logarithmic, and inverse trigonometric functions are covered in Chapter • Calculus: ... variable and multivariable versions • Calculus, Ninth Edition, Metric Version is similar to the present textbook except that the exponential, logarithmic, and inverse trigonometric functions