calculus a complete course ninth edition pdf

Calculus A Complete Course NINTH EDITION www.TechnicalBooksPDF.com 9780134154367_Calculus 05/12/16 3:09 pm This page intentionally left blank www.TechnicalBooksPDF.com A01_LO5943_03_SE_FM.indd iv 04/12/15 4:22 PM ROBERT A ADAMS University of British Columbia CHRISTOPHER ESSEX University of Western Ontario Calculus A Complete Course NINTH EDITION www.TechnicalBooksPDF.com 9780134154367_Calculus 05/12/16 3:09 pm ADAM Editorial dirEctor: Claudine O’Donnell acquisitions Editor: Claudine O’Donnell MarkEting ManagEr: Euan White PrograM ManagEr: Kamilah Reid-Burrell ProjEct ManagEr: Susan Johnson Production Editor: Leanne Rancourt ManagEr of contEnt dEvEloPMEnt: Suzanne Schaan dEvEloPMEntal Editor: Charlotte Morrison-Reed MEdia Editor: Charlotte Morrison-Reed MEdia dEvEloPEr: Kelli Cadet coMPositor: Robert Adams PrEflight sErvicEs: Cenveo® Publisher Services PErMissions ProjEct ManagEr: Joanne Tang intErior dEsignEr: Anthony Leung covEr dEsignEr: Anthony Leung covEr iMagE: © Hiroshi Watanabe / Getty Images vicE-PrEsidEnt, Cross Media and Publishing Services: Gary Bennett Pearson Canada Inc., 26 Prince Andrew Place, Don Mills, Ontario M3C 2T8 Copyright © 2018, 2013, 2010 Pearson Canada Inc All rights reserved Printed in the United States of America This publication is protected by copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise For information regarding permissions, request forms, and the appropriate contacts, please contact Pearson Canada’s Rights and Permissions Department by visiting www pearsoncanada.ca/contact-information/permissions-requests Attributions of third-party content appear on the appropriate page within the text PEARSON is an exclusive trademark owned by Pearson Canada Inc or its affiliates in Canada and/or other countries Unless otherwise indicated herein, any third party trademarks that may appear in this work are the property of their respective owners and any references to third party trademarks, logos, or other trade dress are for demonstrative or descriptive purposes only Such references are not intended to imply any sponsorship, endorsement, authorization, or promotion of Pearson Canada products by the owners of such marks, or any relationship between the owner and Pearson Canada or its affiliates, authors, licensees, or distributors ISBN 978-0-13-415436-7 10 Library and Archives Canada Cataloguing in Publication Adams, Robert A (Robert Alexander), 1940-, author Calculus : a complete course / Robert A Adams, Christopher Essex Ninth edition Includes index ISBN 978-0-13-415436-7 (hardback) Calculus Textbooks I Essex, Christopher, author II Title QA303.2.A33 2017 515 C2016-904267-7 www.TechnicalBooksPDF.com Complete Course_text_cp_template_8-25x10-875.indd 9780134154367_Calculus 16/12/16 pmpm 16/12/162:21 2:53 ADAMS & ESSEX: Calculus: a Complete Course, 8th Edition Front – page v October 14, 2016 To Noreen and Sheran www.TechnicalBooksPDF.com 9780134154367_Calculus 05/12/16 3:09 pm This page intentionally left blank www.TechnicalBooksPDF.com A01_LO5943_03_SE_FM.indd iv 04/12/15 4:22 PM ADAMS & ESSEX: Calculus: a Complete Course, 8th Edition Front – page vii October 14, 2016 vii Contents Preface To the Student To the Instructor Acknowledgments What Is Calculus? xv xvii xviii xix P Preliminaries P.1 Real Numbers and the Real Line Intervals The Absolute Value Equations and Inequalities Involving Absolute Values P.2 Cartesian Coordinates in the Plane Axis Scales Increments and Distances Graphs Straight Lines Equations of Lines 11 12 13 13 15 P.3 Graphs of Quadratic Equations 17 17 19 20 20 20 21 P.4 Functions and Their Graphs 23 The Domain Convention Graphs of Functions Even and Odd Functions; Symmetry and Reflections Reflections in Straight Lines Defining and Graphing Functions with Maple P.5 Combining Functions to Make New Functions 25 26 28 33 P.6 Polynomials and Rational Functions 39 Roots, Zeros, and Factors Roots and Factors of Quadratic Polynomials Miscellaneous Factorings 41 42 P.7 The Trigonometric Functions Some Useful Identities Some Special Angles The Addition Formulas Other Trigonometric Functions 44 46 48 49 51 53 59 59 Average Velocity and Instantaneous Velocity The Growth of an Algal Culture The Area of a Circle 59 One-Sided Limits Rules for Calculating Limits The Squeeze Theorem 1.3 Limits at Infinity and Infinite Limits Limits at Infinity Limits at Infinity for Rational Functions Infinite Limits Using Maple to Calculate Limits 1.4 Continuity Continuity at a Point Continuity on an Interval There Are Lots of Continuous Functions Continuous Extensions and Removable Discontinuities Continuous Functions on Closed, Finite Intervals Finding Roots of Equations 61 62 64 68 69 69 73 73 74 75 77 79 79 81 81 82 83 85 88 Using the Definition of Limit to Prove Theorems Other Kinds of Limits 90 Chapter Review 93 Differentiation 2.1 Tangent Lines and Their Slopes 35 36 54 55 1.1 Examples of Velocity, Growth Rate, and Area 1.5 The Formal Definition of Limit 29 30 33 Sums, Differences, Products, Quotients, and Multiples Composite Functions Piecewise Defined Functions Limits and Continuity 1.2 Limits of Functions 11 Circles and Disks Equations of Parabolas Reflective Properties of Parabolas Scaling a Graph Shifting a Graph Ellipses and Hyperbolas Maple Calculations Trigonometry Review Normals 2.2 The Derivative Some Important Derivatives Leibniz Notation Differentials Derivatives Have the Intermediate-Value Property 2.3 Differentiation Rules Sums and Constant Multiples The Product Rule The Reciprocal Rule The Quotient Rule 90 95 95 99 100 102 104 106 107 108 109 110 112 113 www.TechnicalBooksPDF.com 9780134154367_Calculus 05/12/16 3:09 pm ADAMS & ESSEX: Calculus: a Complete Course, 8th Edition Front – page viii October 14, 2016 ADAM viii 2.4 The Chain Rule 116 Finding Derivatives with Maple Building the Chain Rule into Differentiation Formulas Proof of the Chain Rule (Theorem 6) 2.5 Derivatives of Trigonometric Functions Some Special Limits The Derivatives of Sine and Cosine The Derivatives of the Other Trigonometric Functions 119 119 120 121 121 123 125 2.6 Higher-Order Derivatives 127 2.7 Using Differentials and Derivatives 131 Approximating Small Changes Average and Instantaneous Rates of Change Sensitivity to Change Derivatives in Economics 2.8 The Mean-Value Theorem 131 133 134 135 138 Increasing and Decreasing Functions Proof of the Mean-Value Theorem 2.9 Implicit Differentiation 140 142 145 Higher-Order Derivatives The General Power Rule 148 149 2.10 Antiderivatives and Initial-Value Problems Antiderivatives The Indefinite Integral Differential Equations and Initial-Value Problems 2.11 Velocity and Acceleration 150 150 151 153 Velocity and Speed Acceleration Falling Under Gravity 156 157 160 Chapter Review 163 3.1 Inverse Functions 166 166 Inverting Non–One-to-One Functions Derivatives of Inverse Functions 3.2 Exponential and Logarithmic Functions Exponentials Logarithms 170 170 172 172 173 3.3 The Natural Logarithm and Exponential The Natural Logarithm The Exponential Function General Exponentials and Logarithms Logarithmic Differentiation 3.4 Growth and Decay 176 176 179 181 182 185 The Growth of Exponentials and Logarithms Exponential Growth and Decay Models 3.5 The Inverse Trigonometric Functions The Inverse Sine (or Arcsine) Function The Inverse Tangent (or Arctangent) Function Other Inverse Trigonometric Functions 3.6 Hyperbolic Functions Inverse Hyperbolic Functions 3.7 Second-Order Linear DEs with Constant Coefficients 185 186 188 190 192 192 195 197 200 203 206 Recipe for Solving ay” + by’ + cy = Simple Harmonic Motion Damped Harmonic Motion 206 209 212 Chapter Review 213 More Applications of Differentiation 4.1 Related Rates Procedures for Related-Rates Problems 4.2 Finding Roots of Equations Discrete Maps and Fixed-Point Iteration Newton’s Method “Solve” Routines 216 216 217 222 223 225 229 4.3 Indeterminate Forms 230 l’H^opital’s Rules 231 4.4 Extreme Values 156 Transcendental Functions Interest on Investments Logistic Growth Maximum and Minimum Values Critical Points, Singular Points, and Endpoints Finding Absolute Extreme Values The First Derivative Test Functions Not Defined on Closed, Finite Intervals 4.5 Concavity and Inflections The Second Derivative Test 4.6 Sketching the Graph of a Function Asymptotes Examples of Formal Curve Sketching 4.7 Graphing with Computers Numerical Monsters and Computer Graphing Floating-Point Representation of Numbers in Computers Machine Epsilon and Its Effect on Figure 4.45 Determining Machine Epsilon 4.8 Extreme-Value Problems Procedure for Solving Extreme-Value Problems 236 236 237 238 238 240 242 245 248 247 251 256 256 257 259 260 261 263 www.TechnicalBooksPDF.com 9780134154367_Calculus 05/12/16 3:09 pm ADAMS & ESSEX: Calculus: a Complete Course, 8th Edition Front – page ix October 14, 2016 ix 4.9 Linear Approximations 269 Approximating Values of Functions Error Analysis 4.10 Taylor Polynomials 270 271 275 Taylor’s Formula Big-O Notation Evaluating Limits of Indeterminate Forms 277 280 282 4.11 Roundoff Error, Truncation Error, and Computers 284 Taylor Polynomials in Maple Persistent Roundoff Error Truncation, Roundoff, and Computer Algebra 284 285 286 Chapter Review 287 Integration 291 5.1 Sums and Sigma Notation 291 Evaluating Sums 293 5.2 Areas as Limits of Sums 296 The Basic Area Problem Some Area Calculations 297 298 5.3 The Definite Integral 302 Partitions and Riemann Sums The Definite Integral General Riemann Sums 302 303 305 5.4 Properties of the Definite Integral 307 A Mean-Value Theorem for Integrals Definite Integrals of Piecewise Continuous Functions 5.5 The Fundamental Theorem of Calculus 310 311 313 5.6 The Method of Substitution 319 Trigonometric Integrals 323 5.7 Areas of Plane Regions 327 Areas Between Two Curves 328 Chapter Review 331 Techniques of Integration 334 6.1 Integration by Parts 334 Reduction Formulas 338 6.2 Integrals of Rational Functions 340 Linear and Quadratic Denominators Partial Fractions Completing the Square Denominators with Repeated Factors 6.3 Inverse Substitutions 341 343 345 346 349 The Inverse Trigonometric Substitutions Inverse Hyperbolic Substitutions 349 352 Other Inverse Substitutions The tan(/2) Substitution 6.4 Other Methods for Evaluating Integrals The Method of Undetermined Coefficients Using Maple for Integration Using Integral Tables Special Functions Arising from Integrals 6.5 Improper Integrals Improper Integrals of Type I Improper Integrals of Type II Estimating Convergence and Divergence 6.6 The Trapezoid and Midpoint Rules The Trapezoid Rule The Midpoint Rule Error Estimates 353 354 356 357 359 360 361 363 363 365 368 371 372 374 375 6.7 Simpson’s Rule 378 6.8 Other Aspects of Approximate Integration 382 Approximating Improper Integrals Using Taylor’s Formula Romberg Integration The Importance of Higher-Order Methods Other Methods 383 383 384 387 388 Chapter Review 389 Applications of Integration 393 7.1 Volumes by Slicing—Solids of Revolution 393 Volumes by Slicing Solids of Revolution Cylindrical Shells 394 395 398 7.2 More Volumes by Slicing 402 7.3 Arc Length and Surface Area 406 Arc Length The Arc Length of the Graph of a Function Areas of Surfaces of Revolution 7.4 Mass, Moments, and Centre of Mass Mass and Density Moments and Centres of Mass Two- and Three-Dimensional Examples 7.5 Centroids Pappus’s Theorem 7.6 Other Physical Applications Hydrostatic Pressure Work Potential Energy and Kinetic Energy 7.7 Applications in Business, Finance, and Ecology 406 407 410 413 413 416 417 420 423 425 426 427 430 432 www.TechnicalBooksPDF.com 9780134154367_Calculus 05/12/16 3:09 pm ... (catalogue.pearsoned.ca) Navigate to this book’s catalogue page to view a list of those supplements that are available Speak to your local Pearson sales representative for details and access Also... advantage of a wide range of educational resources by assisting in the integration of a variety of instructional materials and media formats Your local Pearson Canada sales representative can... concept of gateway applications Applications of calculus have always been an important feature of earlier editions of this book But the agenda of introducing gateway applications was introduced