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Calculus Stewart 8th.pdf

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    Contents
    To the Student
    Diagnostic Tests
    A Preview of Calculus
    1 Functions and Models
    1.1 Four Ways to Represent a Function
    1.2 Mathematical Models: A Catalog of Essential Functions
    1.3 New Functions from Old Functions
    1.4 Exponential Functions
    1.5 Inverse Functions and Logarithms
    Review
    Principles of Problem Solving
    2 Limits and Derivatives
    2.1 The Tangent and Velocity Problems
    2.2 The Limit of a Function
    2.3 Calculating Limits Using the Limit Laws
    2.4 The Precise Definition of a Limit
    2.5 Continuity
    2.6 Limits at Infinity; Horizontal Asymptotes
    2.7 Derivatives and Rates of Change
    2.8 The Derivative as a Function
    Review
    Problems Plus
    3 Differentiation Rules
    3.1 Derivatives of Polynomials and Exponential Functions
    3.2 The Product and Quotient Rules
    3.3 Derivatives of Trigonometric Functions
    3.4 The Chain Rule
    3.5 Implicit Defferentiation
    3.6 Derivatives of Logarithmic Functions
    3.7 Rates of CHange in the Natural and Social Sciences
    3.8 Exponential Growth and Decay
    3.9 Related Rates
    3.10 Linear Approximations and Differentials
    3.11 Hyperbolic Functions
    Review
    Problems Plus
    4 Applications of Differentiation
    4.1 Maximum and Minimum Values
    4.2 The Mean Value Theorem
    4.3 How Derivatives Affect the Shape of a Graph
    4.4 Indeterminate Forms and I'Hospital's Rule
    4.5 Summary of Curve Sketching
    4.6 Graphing with Calculus and Calculators
    4.7 Optimization Problems
    4.8 Newton's Method
    4.9 Antiderivatives
    Review
    Problems Plus
    5 Integrals
    5.1 Areas and Distances
    5.2 The Definite Integral
    5.3 The Fundamental Theorem of Calculus
    5.4 Indefinite Integrals and the Net Change Theorem
    5.5 The Substitution Rule
    Review
    Problems Plus
    6 Applications of Integration
    6.1 Areas Between Curves
    6.2 Volumes
    6.3 Volumes by Cylindrical Shells
    6.4 Work
    6.5 Average Value of a Function
    Review
    Problems Plus
    7 Techniques of Integration
    7.1 Integration by Parts
    7.2 Trigonometric Integrals
    7.3 Trigonometiric Substitution
    7.4 Integration of Rational Functions by Partial Fractions
    7.5 Strategy for Integration
    7.6 Integration Using Tables and Computer Algebra Systems
    7.7 Approximate Integration
    7.8 Improper Integrals
    Review
    Problems Plus
    8 Further Applications of Integration
    8.1 Arc Length
    8.2 Area of a Surface of Revolution
    8.3 Applications to Physics and Engineering
    8.4 Applications to Economics and Biology
    8.5 Probability
    Review
    Problems Plus
    9 Differential Equations
    9.1 Modeling with Differential Equations
    9.2 Direction Fields and Euler's Method
    9.3 Separable Equations
    9.4 Models for Poulation Growth
    9.5 Linear Equations
    9.6 Predator-Prey Systems
    Review
    Problems Plus
    10 Parametric Equations and Polar Coordinates
    10.1 Curves Defined by Parametric Equations
    10.2 Calculus with Parametric Curves
    10.3 Polar Coordinates
    10.4 Areas and Lengths in Polar Coordinates
    10.5 Conic Sections
    10.6 Conic Sections in Polar Coordinates
    Review
    Problems Plus
    11 Infinite Sequences and Series
    11.1 Sequences
    11.2 Series
    11.3 The Integral Test and Estimates of Sums
    11.4 The Comparison Tests
    11.5 Altenating Series
    11.6 Absolute Convergence and the Radio and Root Tests
    11.7 Strategy for Testing Series
    11.8 Power Series
    11.9 Representations of FUnctions as Power Series
    11.10 Taylor and Maclaurin Series
    11.11 Applications of Taylor Polynomials
    Review
    Problems Plus
    12 Vectors and the Geometry of Space
    12.1 Thre-Dimensional Coordinate Systems
    12.2 Vectors
    12.3 The Dot Product
    12.4 The Cross Product
    12.5 Equations of Lines and Planes
    12.6 Cylinders and Quadric Surfaces
    Review
    Problems Plus
    13 Vector Functions
    13.1 Vector Functions and Space Curves
    13.2 Derivatives and Integrals of Vector Functions
    13.3 Arc Length and Curvature
    13.4 Motion in Space: Velocity and Acceleration
    Review
    Problems Plus
    14 Partial Derivatives
    14.1 Functions of Several Variables
    14.2 Limits and Continuity
    14.3 Partial Derivatives
    14.4 Tangent Planes and Linear Approximations
    14.5 The Chain Rule
    14.6 Directional Derivatives and the Gradient Vector
    14.7 Maximum and Minimum Values
    14.8 Lagrange Multipliers
    Review
    Problems Plus
    15 Multiple Integrals
    15.1 Double Integrals over Rectangles
    15.2 Double Integrals over General Regions
    15.3 Double Integrals in Polar Coordinates
    15.4 Applications of Double Integrals
    15.5 Surface Area
    15.6 Triple Integrals
    15.7 Triple Integrals in Cylindrical Coordinates
    15.8 Triple Integrals in Spherical Coordinates
    15.9 Change of Variables in Multiple Integrals
    Review
    Problems Plus
    16 Vector Calculus
    16.1 Vector Fields
    16.2 Line Integrals
    16.3 The Fundamental Theorem for Line Integrals
    16.4 Green's Theorem
    16.5 Curl and Divergence
    16.6 Parametric Surface and Their Areas
    16.7 Surface Integrals
    16.8 Stokes' Theorem
    16.9 The Divergence Theorem
    16.10 Summary
    Review
    Problems Plus
    17 Second-Order Defferential Equations
    17.1 Second-Order Linear Equations
    17.2 Nonhomogeneous Linear Equations
    17.3 Applications of Second-Order Differential Equations
    17.4 Series Solutions
    Review
    Appendixes
    A Numbers, Inequalities, and Absolute Values
    B Coordinate Geometry and Lines
    C Graphs of Second-Degree Equations
    D Trigonometry
    E Sigma Notation
    F Proofs of Theorems
    G The Logarithm Defined as Integral
    H Complex Numbers
    I Answers to Odd-Numbered Exercises
    Index
    CALCULUSEARLY TRANSCENDENTALSEIGHTH EDITIONJAMES STEWARTMCMASTER UNIVERSITY AND UNIVERSITY OF TORONTOCopyright 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.
    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. portant otice eia content reference ithin the proct escription or the proct tet a not e availale in the eoo version Copyright 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.
    Printed in the United States of AmericaPrint Number: 01 Print Year: 2014K12T14Calculus: Early Transcendentals, Eighth EditionJames StewartProduct Manager: Neha TalejaSenior Content Developer: Stacy GreenAssociate Content Developer: Samantha LugtuProduct Assistant: Stephanie KreuzMedia Developer: Lynh PhamMarketing Manager: Ryan AhernContent 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 ImagesWindows is a registered trademark of the Microsoft Corporation and used herein 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.© 2016, 2012 Cengage LearningALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher.For product information and technology assistance, contact us atCengage Learning Customer & Sales Support, 1-800-354-9706.F swww.cengage.com/permissions.F permissionrequest@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 02210 USACengage 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.Cengage Learning products are represented in Canada by Nelson Education, Ltd.To learn more about Cengage Learning Solutions, visit www.cengage.com.Purchase any of our products at your local college store or at our pre-ferred online store www.cengagebrain.com.WCN: 02-200-203Copyright 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.
    iiiPREFACE xiTO THE STUDENT xxiiiCALCULATORS, COMPUTERS, AND OTHER GRAPHING DEVICES xxivDIAGNOSTIC TESTS xxviA Preview of Calculus 11 1.1 Four Ways to Represent a Function 10 1.2 Mathematical Models: A Catalog of Essential Functions 23 1.3 New Functions from Old Functions 36 1.4 Exponential Functions 45 1.5 Inverse Functions and Logarithms 55 Review 68 Principles of Problem Solving 712 2.1 The Tangent and Velocity Problems 78 2.2 The Limit of a Function 83 2.3 Calculating Limits Using the Limit Laws 95 2.4 The Precise Definition of a Limit 104 2.5 Continuity 114 2.6 Limits at Infinity; Horizontal Asymptotes 126 2.7 Derivatives and Rates of Change 140 Early Methods for Finding Tangents 152 2.8 The Derivative as a Function 152 Review 165 Problems Plus 169ContentsCopyright 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.
    3 3.1 Derivatives of Polynomials and Exponential Functions 172 Building a Better Roller Coaster 182 3.2 The Product and Quotient Rules 183 3.3 Derivatives of Trigonometric Functions 190 3.4 The Chain Rule 197 Where Should a Pilot Start Descent? 208 3.5 Implicit Differentiation 208 Families of Implicit Curves 217 3.6 Derivatives of Logarithmic Functions 218 3.7 Rates of Change in the Natural and Social Sciences 224 3.8 Exponential Growth and Decay 237 Controlling Red Blood Cell Loss During Surgery 244 3.9 Related Rates 245 3.10 Linear Approximations and Differentials 251 Taylor Polynomials 258 3.11 Hyperbolic Functions 259 Review 266 Problems Plus 2704 4.1 Maximum and Minimum Values 276 The Calculus of Rainbows 285 4.2 The Mean Value Theorem 287 4.3 How Derivatives Affect the Shape of a Graph 293 4.4 Indeterminate Forms and l’Hospital’s Rule 304 The Origins of l’Hospital’s Rule 314 4.5 Summary of Curve Sketching 315 4.6 Graphing with Calculus and Calculators 323 4.7 Optimization Problems 330 The Shape of a Can 343 Planes and Birds: Minimizing Energy 344 4.8 Newton’s Method 345 4.9 Antiderivatives 350 Review 358 Problems Plus 363iv ContentsCopyright 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.
    Contents v5 5.1 Areas and Distances 366 5.2 The Definite Integral 378 Area Functions 391 5.3 The Fundamental Theorem of Calculus 392 5.4 Indefinite Integrals and the Net Change Theorem 402 Newton, Leibniz, and the Invention of Calculus 411 5.5 The Substitution Rule 412 Review 421 Problems Plus 4256 6.1 Areas Between Curves 428 The Gini Index 436 6.2 Volumes 438 6.3 Volumes by Cylindrical Shells 449 6.4 Work 455 6.5 Average Value of a Function 461 Calculus and Baseball 464 Where to Sit at the Movies 465 Review 466 Problems Plus 4687 7.1 Integration by Parts 472 7.2 Trigonometric Integrals 479 7.3 Trigonometric Substitution 486 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 Patterns in Integrals 513 7.7 Approximate Integration 514 7.8 Improper Integrals 527 Review 537 Problems 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.
    vi Contents8 8.1 Arc Length 544 Arc Length Contest 550 8.2 Area of a Surface of Revolution 551 Rotating on a Slant 557 8.3 Applications to Physics and Engineering 558 Complementary Coffee Cups 568 8.4 Applications to Economics and Biology 569 8.5 Probability 573 Review 581 Problems Plus 5839 9.1 Modeling with Differential Equations 586 9.2 Direction Fields and Euler’s Method 591 9.3 Separable Equations 599 How Fast Does a Tank Drain? 608 Which Is Faster, Going Up or Coming Down? 609 9.4 Models for Population Growth 610 9.5 Linear Equations 620 9.6 Predator-Prey Systems 627 Review 634 Problems Plus 63710 10.1 Curves Defined by Parametric Equations 640 Running Circles Around Circles 648 10.2 Calculus with Parametric Curves 649 Bézier Curves 657 10.3 Polar Coordinates 658 Families of Polar Curves 668 10.4 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.
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