第1页 / 共1406页
第2页 / 共1406页
第3页 / 共1406页
第4页 / 共1406页
第5页 / 共1406页
第6页 / 共1406页
第7页 / 共1406页
第8页 / 共1406页
Calculus.pdf
Contents
Preface
To the Student
Calculators, Computers, and Other Graphing Devices
Diagnostic Tests
A Preview of Calculus
Ch 1: Functions and Limits
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: The Tangent and Velocity Problems
1.5: The Limit of a Function
1.6: Calculating Limits Using the Limit Laws
1.7: The Precise Definition of a Limit
1.8: Continuity
Review
Principles of Problem Solving
Ch 2: Derivatives
2.1: Derivatives and Rates of Change
2.2: The Derivative as a Function
2.3: Differentiation Formulas
2.4: Derivatives of Trigonometric Functions
2.5: The Chain Rule
2.6: Implicit Differentiation
2.7: Rates of Change in the Natural and Social Sciences
2.8: Related Rates
2.9: Linear Approximations and Differentials
Review
Problems Plus
Ch 3: Applications of Differentiation
3.1: Maximum and Minimum Values
3.2: The Mean Value Theorem
3.3: How Derivatives Affect the Shape of a Graph
3.4: Limits at Infinity; Horizontal Asymptotes
3.5: Summary of Curve Sketching
3.6: Graphing with Calculus and Calculators
3.7: Optimization Problems
3.8: Newton's Method
3.9: Antiderivatives
Review
Problems Plus
Ch 4: Integrals
4.1: Areas and Distances
4.2: The Definite Integral
4.3: The Fundamental Theorem of Calculus
4.4: Indefinite Integrals and the Net Change Theorem
4.5: The Substitution Rule
Review
Problems Plus
Ch 5: Applications of Integration
5.1: Areas between Curves
5.2: Volumes
5.3: Volumes by Cylindrical Shells
5.4: Work
5.5: Average Value of a Function
Review
Problems Plus
Ch 6: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
6.1: Inverse Functions
6.2: Exponential Functions and Their Derivatives
6.3: Logarithmic Functions
6.4: Derivatives of Logarithmic Functions
6.2*: The Natural Logarithmic Function
6.3*: The Natural Exponential Function
6.4*: General Logarithmic and Exponential Functions
6.5: Exponential Growth and Decay
6.6: Inverse Trigonometric Functions
6.7: Hyperbolic Functions
6.8: Indeterminate Forms and l'Hospital's Rule
Review
Problems Plus
Ch 7: Techniques of Integration
7.1: Integration by Parts
7.2: Trigonometric Integrals
7.3: Trigonometric 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
Ch 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
Ch 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 Population Growth
9.5: Linear Equations
9.6: Predator-Prey Systems
Review
Problems Plus
Ch 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
Ch 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: Alternating Series
11.6: Absolute Convergence and the Ratio 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
Ch 12: Vectors and the Geometry of Space
12.1: Three-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
Ch 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
Ch 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
Ch 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
Ch 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 Surfaces and Their Areas
16.7: Surface Integrals
16.8: Stokes' Theorem
16.9: The Divergence Theorem
16.10: Summary
Review
Problems Plus
Ch 17: Second-Order Differential 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
Appendix A: Numbers, Inequalities, and Absolute Values
Appendix B: Coordinate Geometry and Lines
Appendix C: Graphs of Second-Degree Equations
Appendix D: Trigonometry
Appendix E: Sigma Notation
Appendix F: Proofs of Theorems
Appendix G: Complex Numbers
Appendix H: Answers to Odd-Numbered Exercises
Index
CALCULUSEIGHTH 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: 2015K04T15Calculus, 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: 2015937035Student Edition:ISBN: 978-1-285-74062-1Loose-leaf Edition:ISBN: 978-1-305-27176-0Cengage Learning20 Channel Center StreetBoston, MA 02210 USACengage Learning is a leading provider of customized learning solutions with employees residing in nearly 40 different countries and sales in more than 125 countries around the world. Find your local representative at www.cengage.com.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.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.WCN: 02-200-203
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 The Tangent and Velocity Problems 45 1.5 The Limit of a Function 50 1.6 Calculating Limits Using the Limit Laws 62 1.7 The Precise Definition of a Limit 72 1.8 Continuity 82 Review 94 Principles of Problem Solving 982 2.1 Derivatives and Rates of Change 106 Early Methods for Finding Tangents 117 2.2 The Derivative as a Function 117 2.3 Differentiation Formulas 130 95 Building a Better Roller Coaster 144 2.4 Derivatives of Trigonometric Functions 144 2.5 The Chain Rule 152 Where Should a Pilot Start Descent? 161 2.6 Implicit Differentiation 161 Families of Implicit Curves 168ContentsCopyright 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.
2.7 Rates of Change in the Natural and Social Sciences 169 2.8 Related Rates 181 2.9 Linear Approximations and Differentials 188 Taylor Polynomials 194 Review 195 Problems Plus 2003 3.1 Maximum and Minimum Values 204 The Calculus of Rainbows 213 3.2 The Mean Value Theorem 215 3.3 How Derivatives Affect the Shape of a Graph 221 3.4 Limits at Infinity; Horizontal Asymptotes 231 3.5 Summary of Curve Sketching 244 3.6 Graphing with Calculus and Calculators 251 3.7 Optimization Problems 258 The Shape of a Can 270 Planes and Birds: Minimizing Energy 271 3.8 Newton’s Method 272 3.9 Antiderivatives 278 Review 285 Problems Plus 2894 4.1 Areas and Distances 294 4.2 The Definite Integral 306 Area Functions 319 4.3 The Fundamental Theorem of Calculus 320 4.4 Indefinite Integrals and the Net Change Theorem 330 Newton, Leibniz, and the Invention of Calculus 339 4.5 The Substitution Rule 340 Review 348 Problems Plus 352iv 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 Between Curves 356 The Gini Index 364 5.2 Volumes 366 5.3 Volumes by Cylindrical Shells 377 5.4 Work 383 5.5 Average Value of a Function 389 Calculus and Baseball 392 Review 393 Problems Plus 3956 6.1 Inverse Functions 400 Instructors may cover either Sections 6.2–6.4 or Sections 6.2*–6.4*. See the Preface.6.2Exponential Functions and Their Derivatives 4086.2*The Natural Logarithmic Function 4386.3Logarithmic Functions 4216.3*The Natural Exponential Function 4476.4Derivatives of Logarithmic Functions 4286.4*General Logarithmic and Exponential Functions 455 6.5 Exponential Growth and Decay 466 Controlling Red Blood Cell Loss During Surgery 473 6.6 Inverse Trigonometric Functions 474 Where to Sit at the Movies 483 6.7 Hyperbolic Functions 484 6.8 Indeterminate Forms and l’Hospital’s Rule 491 The Origins of l’Hospital’s Rule 503 Review 503 Problems Plus 508Copyright 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 Contents7 7.1 Integration by Parts 512 7.2 Trigonometric Integrals 519 7.3 Trigonometric Substitution 526 7.4 Integration of Rational Functions by Partial Fractions 533 7.5 Strategy for Integration 543 7.6 Integration Using Tables and Computer Algebra Systems 548 Patterns in Integrals 553 7.7 Approximate Integration 554 7.8 Improper Integrals 567 Review 577 Problems Plus 5808 8.1 Arc Length 584 Arc Length Contest 590 8.2 Area of a Surface of Revolution 591 Rotating on a Slant 597 8.3 Applications to Physics and Engineering 598 Complementary Coffee Cups 608 8.4 Applications to Economics and Biology 609 8.5 Probability 613 Review 621 Problems Plus 6239 9.1 Modeling with Differential Equations 626 9.2 Direction Fields and Euler’s Method 631 9.3 Separable Equations 639 How Fast Does a Tank Drain? 648 Which Is Faster, Going Up or Coming Down? 649 9.4 Models for Population Growth 650 9.5 Linear Equations 660Copyright 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.
相关推荐
2023年江西萍乡中考道德与法治真题及答案.doc
2012年重庆南川中考生物真题及答案.doc
2013年江西师范大学地理学综合及文艺理论基础考研真题.doc
2020年四川甘孜小升初语文真题及答案I卷.doc
2020年注册岩土工程师专业基础考试真题及答案.doc
2023-2024学年福建省厦门市九年级上学期数学月考试题及答案.doc
2021-2022学年辽宁省沈阳市大东区九年级上学期语文期末试题及答案.doc
2022-2023学年北京东城区初三第一学期物理期末试卷及答案.doc
2018上半年江西教师资格初中地理学科知识与教学能力真题及答案.doc
2012年河北国家公务员申论考试真题及答案-省级.doc
2020-2021学年江苏省扬州市江都区邵樊片九年级上学期数学第一次质量检测试题及答案.doc
2022下半年黑龙江教师资格证中学综合素质真题及答案.doc
