Calculus: Early Transcendentals (Stewart), 8th Ed.
calculusEarly Transcendentalseighth editionJames StewartM c Master UniversityandUniversity of TorontoAustralia Brazil Mexico Singapore United Kingdom United StatesCopyright 2016 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.
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Calculus: Early Transcendentals, Eighth EditionJames Stewart 2016, 2012 Cengage LearningProduct Manager: Neha TalejaALL RIGHTS RESERVED. No part of this work covered by the copyrightherein may be reproduced, transmitted, stored, or used in any form or byany means graphic, electronic, or mechanical, including but not limited tophotocopying, recording, scanning, digitizing, taping, Web distribution,information networks, or information storage and retrieval systems, exceptas permitted under Section 107 or 108 of the 1976 United States CopyrightAct, without the prior written permission of the publisher.Senior Content Developer: Stacy GreenAssociate Content Developer: Samantha LugtuProduct Assistant: Stephanie KreuzMedia Developer: Lynh PhamMarketing Manager: Ryan AhernWCN: 02-200-203Content Project Manager: Cheryll LinthicumArt Director: Vernon BoesManufacturing Planner: Becky CrossProduction Service: TECHartsPhoto and Text Researcher: Lumina DatamaticsCopy Editor: Kathi Townes, TECHartsIllustrator: TECHartsText Designer: Diane BeasleyCover Designer: Irene Morris, Morris DesignCompositor: Stephanie Kuhns, Kristina Elliott,and Kira Abdallah, TECHartsCover Image: elisanth/123RF; tharrison/Getty ImagesFor product information and technology assistance, contact us atCengage Learning Customer & Sales Support, 1-800-354-9706.For permission to use material from this text or product,submit all requests online at www.cengage.com/permissions.Further permissions questions can be e-mailed topermissionrequest@cengage.com.Library of Congress Control Number: 2014951195Student Edition:ISBN: 978-1-285-74155-0Loose-leaf Edition:ISBN: 978-1-305-27235-4Cengage Learning20 Channel Center StreetBoston, MA 02210USACengage Learning is a leading provider of customized learning solutionswith office locations around the globe, including Singapore, the UnitedKingdom, Australia, Mexico, Brazil, and Japan. Locate your local office atwww.cengage.com/global.Cengage Learning products are represented in Canada byNelson Education, Ltd.Windows is a registered trademark of the Microsoft Corporation and usedherein under license.Macintosh is a registered trademark of Apple Computer, Inc.Used herein under license.Maple is a registered trademark of Waterloo Maple, Inc.Mathematica is a registered trademark of Wolfram Research, Inc.Tools for Enriching Calculus is a trademark used herein under license.Printed in the United States of AmericaPrint Number: 01 Print Year: 2014Copyright 2016 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.k12T14To learn more about Cengage Learning Solutions, visit www.cengage.com.Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com.
ContentsPreface xiTo the Student xxiiiCalculators, Computers, and other graphing devicesDiagnostic testsxxivxxviA Preview of Calculus 111.11.21.31.41.5Four Ways to Represent a Function 10Mathematical Models: A Catalog of Essential Functions 23New Functions from Old Functions 36Exponential Functions 45Inverse Functions and Logarithms 55Review 68Principles of Problem Solving 7122.1 The Tangent and Velocity Problems 782.2 The Limit of a Function 832.3 Calculating Limits Using the Limit Laws 952.4 The Precise Definition of a Limit 1042.5 Continuity 1142.6 Limits at Infinity; Horizontal Asymptotes 1262.7 Derivatives and Rates of Change 140Writing Project Early Methods for Finding Tangents 1522.8 The Derivative as a Function 152Review 165Problems Plus 169iiiCopyright 2016 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.
ivContents33.1Derivatives of Polynomials and Exponential Functions 172Applied Project Building a Better Roller Coaster 1823.2 The Product and Quotient Rules 1833.3 Derivatives of Trigonometric Functions 1903.4 The Chain Rule 197Applied Project Where Should a Pilot Start Descent? 2083.5 Implicit Differentiation 208Laboratory Project Families of Implicit Curves 2173.6 Derivatives of Logarithmic Functions 2183.7 Rates of Change in the Natural and Social Sciences 2243.8 Exponential Growth and Decay 237Applied Project Controlling Red Blood Cell Loss During Surgery 2443.9 Related Rates 2453.10 Linear Approximations and Differentials 251Laboratory Project Taylor Polynomials 2583.11 Hyperbolic Functions 259Review 266Problems Plus 27044.14.24.34.44.54.64.74.84.9Maximum and Minimum Values 276Applied Project The Calculus of Rainbows 285The Mean Value Theorem 287How Derivatives Affect the Shape of a Graph 293Indeterminate Forms and l’Hospital’s Rule 304Writing Project The Origins of l’Hospital’s Rule 314Summary of Curve Sketching 315Graphing with Calculus and Calculators 323Optimization Problems 330Applied Project The Shape of a Can 343Applied Project Planes and Birds: Minimizing Energy 344Newton’s Method 345Antiderivatives 350Review 358Problems Plus 363Copyright 2016 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.
Contents55.15.2Areas and Distances 366The Definite Integral 378Discovery Project Area Functions 3915.3 The Fundamental Theorem of Calculus 3925.4 Indefinite Integrals and the Net Change Theorem 402Writing Project Newton, Leibniz, and the Invention of Calculus 4115.5 The Substitution Rule 412Review 421Problems Plus 42566.16.26.36.46.5Areas Between Curves 428Applied Project The Gini Index 436Volumes 438Volumes by Cylindrical Shells 449Work 455Average Value of a Function 461Applied Project Calculus and Baseball 464Applied Project Where to Sit at the Movies 465Review 466Problems Plus 46877.17.27.37.47.57.6Integration by Parts 472Trigonometric Integrals 479Trigonometric Substitution 486Integration of Rational Functions by Partial Fractions 493Strategy for Integration 503Integration Using Tables and Computer Algebra Systems 508Discovery Project Patterns in Integrals 5137.7 Approximate Integration 5147.8 Improper Integrals 527Review 537Problems Plus 540Copyright 2016 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.v
viContents88.18.28.38.48.5Arc Length 544Discovery Project Arc Length Contest 550Area of a Surface of Revolution 551Discovery Project Rotating on a Slant 557Applications to Physics and Engineering 558Discovery Project Complementary Coffee Cups 568Applications to Economics and Biology 569Probability 573Review 581Problems Plus 58399.19.29.3Modeling with Differential Equations 586Direction Fields and Euler’s Method 591Separable Equations 599Applied Project How Fast Does a Tank Drain? 608Applied Project Which Is Faster, Going Up or Coming Down? 6099.4 Models for Population Growth 6109.5 Linear Equations 6209.6 Predator-Prey Systems 627Review 634Problems Plus 6371010.1 Curves Defined by Parametric Equations 640Laboratory Project Running Circles Around Circles 64810.2 Calculus with Parametric Curves 649Laboratory Project Bézier Curves 65710.3 Polar Coordinates 658Laboratory Project Families of Polar Curves 66810.4 Areas and Lengths in Polar Coordinates 669Copyright 2016 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.
Contents10.510.6Conic Sections 674Conic Sections in Polar Coordinates 682Review 689Problems Plus 6921111.1 Sequences 694Laboratory Project Logistic Sequences 70711.2 Series 70711.3 The Integral Test and Estimates of Sums 71911.4 The Comparison Tests 72711.5 Alternating Series 73211.6 Absolute Convergence and the Ratio and Root Tests 73711.7 Strategy for Testing Series 74411.8 Power Series 74611.9 Representations of Functions as Power Series 75211.10 Taylor and Maclaurin Series 759Laboratory Project An Elusive Limit 773Writing Project How Newton Discovered the Binomial Series 77311.11 Applications of Taylor Polynomials 774Applied Project Radiation from the Stars 783Review 784Problems Plus 7871212.1 Three-Dimensional Coordinate Systems 79212.2 Vectors 79812.3 The Dot Product 80712.4 The Cross Product 814Discovery Project The Geometry of a Tetrahedron 82312.5 Equations of Lines and Planes 823Laboratory Project Putting 3D in Perspective 83312.6 Cylinders and Quadric Surfaces 8347et1206un0304/21/10MasterID: 01462Review 841Problems Plus 844Copyright 2016 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.vii
viiiContents1313.1 Vector Functions and Space Curves 84813.2 Derivatives and Integrals of Vector Functions 85513.3 Arc Length and Curvature 86113.4 Motion in Space: Velocity and Acceleration 870Applied Project Kepler’s Laws 880Review 881Problems Plus 8841414.1 Functions of Several Variables 88814.2 Limits and Continuity 90314.3 Partial Derivatives 91114.4 Tangent Planes and Linear Approximations 927Applied Project The Speedo LZR Racer 93614.5 The Chain Rule 93714.6 Directional Derivatives and the Gradient Vector 94614.7 Maximum and Minimum Values 959Applied Project Designing a Dumpster 970Discovery Project Quadratic Approximations and Critical Points 97014.8 Lagrange Multipliers 971Applied Project Rocket Science 979Applied Project Hydro-Turbine Optimization 980Review 981Problems Plus 9851515.115.215.315.415.5Double Integrals over Rectangles 988Double Integrals over General Regions 1001Double Integrals in Polar Coordinates 1010Applications of Double Integrals 1016Surface Area 1026Copyright 2016 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.
Contents15.6 Triple Integrals 1029Discovery Project Volumes of Hyperspheres 104015.7 Triple Integrals in Cylindrical Coordinates 1040Discovery Project The Intersection of Three Cylinders 104415.8 Triple Integrals in Spherical Coordinates 1045Applied Project Roller Derby 105215.9 Change of Variables in Multiple Integrals 1052Review 1061Problems Plus 10651616.1 Vector Fields 106816.2 Line Integrals 107516.3 The Fundamental Theorem for Line Integrals 108716.4 Green’s Theorem 109616.5 Curl and Divergence 110316.6 Parametric Surfaces and Their Areas 111116.7 Surface Integrals 112216.8 Stokes’ Theorem 1134Writing Project Three Men and Two Theorems 114016.9 The Divergence Theorem 114116.10 Summary 1147Review 1148Problems Plus 11511717.117.217.317.4Second-Order Linear Equations 1154Nonhomogeneous Linear Equations 1160Applications of Second-Order Differential Equations 1168Series Solutions 1176Review 1181Copyright 2016 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.ix
xContentsABCDEFGHINumbers, Inequalities, and Absolute Values A2Coordinate Geometry and Lines A10Graphs of Second-Degree Equations A16Trigonometry A24Sigma Notation A34Proofs of Theorems A39The Logarithm Defined as an Integral A50Complex Numbers A57Answers to Odd-Numbered Exercises A65Copyright 2016 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.
PrefaceA great discovery solves a great problem but there is a grain of discovery in thesolution of any problem. Your problem may be modest; but if it challenges yourcuriosity and brings into play your inventive faculties, and if you solve it by yourown means, you may experience the tension and enjoy the triumph of discovery.g e o r g e p o lyaThe art of teaching, Mark Van Doren said, is the art of assisting discovery. I have triedto write a book that assists students in discovering calculus—both for its practical powerand its surprising beauty. In this edition, as in the first seven editions, I aim to conveyto the student a sense of the utility of calculus and develop technical competence, but Ialso strive to give some appreciation for the intrinsic beauty of the subject. Newtonundoubtedly experienced a sense of triumph when he made his great discoveries. I wantstudents to share some of that excitement.The emphasis is on understanding concepts. I think that nearly everybody agrees thatthis should be the primary goal of calculus instruction. In fact, the impetus for the current calculus reform movement came from the Tulane Conference in 1986, which formulated as their first recommendation:Focus on conceptual understanding.I have tried to implement this goal through the Rule of Three: “Topics should be presented geometrically, numerically, and algebraically.” Visualization, numerical andgraphical experimentation, and other approaches have changed how we teach conceptual reasoning in fundamental ways. More recently, the Rule of Three has been expandedto become the Rule of Four by emphasizing the verbal, or descriptive, point of view aswell.In writing the eighth edition my premise has been that it is possible to achieve conceptual understanding and still retain the best traditions of traditional calculus. The bookcontains elements of reform, but within the context of a traditional curriculum.I have written several other calculus textbooks that might be preferable for some instructors. Most of them also come in single variable and multivariable versions. Calculus, Eighth Edition, is similar to the present textbook except that the exponential, logarithmic, and inverse trigonometric functions are covered in the secondsemester.Essential Calculus, Second Edition, is a much briefer book (840 pages), though itcontains almost all of the topics in Calculus, Eighth Edition. The relative brevity isachieved through briefer exposition of some topics and putting some features on thewebsite.Essential Calculus: Early Transcendentals, Second Edition, resembles EssentialCalculus, but the exponential, logarithmic, and inverse trigonometric functions arecovered in Chapter 3.xiCopyright 2016 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.
xiiPreface Calculus: Concepts and Contexts, Fourth Edition, emphasizes conceptual understanding even more strongly than this book. The coverage of topics is not encyclopedic and the material on transcendental functions and on parametric equations iswoven throughout the book instead of being treated in separate chapters.Calculus: Early Vectors introduces vectors and vector functions in the first semesterand integrates them throughout the book. It is suitable for students taking engineering and physics courses concurrently with calculus.Brief Applied Calculus is intended for students in business, the social sciences, andthe life sciences.Biocalculus: Calculus for the Life Sciences is intended to show students in the lifesciences how calculus relates to biology.Biocalculus: Calculus, Probability, and Statistics for the Life Sciences contains allthe conte
4.3 How Derivatives Affect the Shape of a Graph 293 4.4 Indeterminate Forms and l’Hospital’s Rule 304 . 7.4 Integration of Rational Functions by Partial Fractions 493 7.5 Strategy for Integration 503 7.6 Integration Using Tables and Computer Algebra Systems 508
Calculus: Early Transcendentals. James Stewart, Seventh ed. A graphing calculator (I will be using a TI-84) Regular, reliable internet access for completing online homework assignments Notebook for homework. You will need graph paper/sticky notes or engineering paper Optional materials: Graphing Calculator Manual, by Dennis Pence
MATH 210 Single Variable Calculus I Early Transcendentals (4) o Allan Hancock College : MATH 181 Calculus 1 5 o American River College : MATH 400 Calculus I 5 o Berkeley City College : MATH 3A Calculus I 5 o Cabrillo College : MATH 5A Analytic Geometry and Calculus I 5 o Canada College : MATH 251 Analytical Geometry and Calculus I 5
Stewart, Calculus: Early Transcendentals, 8th Edition. 2016 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly .
Analytical Geometry & Calculus I, II, & III MAT 221, 231, & 241 (Revision: July 2017) MAT221 Course Information Course Description: An introduction to analytic geometry, limits, continuity, differential and integral calculus of single variable functions, and related applications. Title: Thomas’ Calculus Early Transcendentals, Single Variables, 14th edition Author: Weir & Hass Publisher .
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