University Calculus: Early Transcendentals (4th Edition) PDF
Preview University Calculus: Early Transcendentals (4th Edition)
UNIVERSITY CALCULUS EARLY TRANSCENDENTALS HASS • HEIL • BOGACKI • WEIR • THOMAS FOURTH EDITION MyLab Math for University Calculus, 4e (access code required) MyLab™ Math is the teaching and learning platform that empowers instructors to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math for University Calculus, 4e personalizes the learning experience and improves results for each student. Interactive Figures A full suite of Interactive Figures was added to illustrate key concepts and allow manipulation. Designed in the freely available G eoGebra software, these figures can be used in lecture as well as by students independently. Questions that Deepen U nderstanding MyLab Math includes a variety of question types designed to help students succeed in the course. In Setup & Solve questions, students show how they set up a problem as well as the solution, better mirroring what is required on tests. Additional Conceptual Questions were written by faculty at Cornell University to support deeper, theoretical understanding of the key concepts in calculus. Learning Catalytics Now included in all MyLab Math courses, this student response tool uses smartphones, tablets, or laptops to engage students in more interactive tasks and thinking during lecture. Learning Catalytics™ fosters student engagement and peer-to-peer learning with real-time analytics. pearson.com/mylab/math A02_HASS5540_15_SE_FEP.indd 1 01/11/18 4:30 PM U N I V E R S I T Y C A L C U L U S EARLY TRANSCENDENTALS Fourth Edition Joel Hass University of California, Davis Christopher Heil Georgia Institute of Technology Przemyslaw Bogacki Old Dominion University Maurice D. Weir Naval Postgraduate School George B. Thomas, Jr. Massachusetts Institute of Technology A01_HASS5540_15_SE_FM.indd 1 03/11/2018 05:24 Director, Portfolio Management: Deirdre Lynch Executive Editor: Jeff Weidenaar Editorial Assistant: Jonathan Krebs Content Producer: Rachel S. Reeve Managing Producer: Scott Disanno Producer: Shannon Bushee Manager, Courseware QA: Mary Durnwald Manager, Content Development: Kristina Evans Product Marketing Manager: Emily Ockay Product Marketing Assistant: Shannon McCormack Field Marketing Manager: Evan St. Cyr Senior Author Support/Technology Specialist: Joe Vetere Manager, Rights and Permissions: Gina Cheselka Text and Cover Design: Pearson CSC Full Service Vendor: Pearson CSC Full Service Project Management: Julie Kidd, Pearson CSC Manufacturing Buyer: Carol Melville, LSC Communications Cover Image: Steve Mann/123RF Copyright © 2020, 2016, 2012 by Pearson Education, Inc. 221 River Street, Hoboken, NJ 07030. All Rights Reserved. Printed in the United States of America. 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Cataloging-in-Publication Data on file with the Library of Congress. 1 19 Instructor’s Edition ISBN 13: 978-0-13-516487-7 ISBN 10: 0-13-516487-7 Student’s Edition ISBN 13: 978-0-13-499554-0 ISBN 10: 0-13-499554-6 A01_HASS5540_15_SE_FM.indd 2 05/12/18 1:08 PM Contents Preface ix 1 Functions 1 1.1 Functions and Their Graphs 1 1.2 Combining Functions; Shifting and Scaling Graphs 14 1.3 Trigonometric Functions 21 1.4 Graphing with Software 29 1.5 Exponential Functions 33 1.6 Inverse Functions and Logarithms 38 Also available: A.1 Real Numbers and the Real Line, A.3 Lines and Circles 2 Limits and Continuity 51 2.1 Rates of Change and Tangent Lines to Curves 51 2.2 Limit of a Function and Limit Laws 58 2.3 The Precise Definition of a Limit 69 2.4 One-Sided Limits 78 2.5 Continuity 85 2.6 Limits Involving Infinity; Asymptotes of Graphs 97 Questions to Guide Your Review 110 Practice Exercises 111 Additional and Advanced Exercises 113 Also available: A.5 Proofs of Limit Theorems 3 Derivatives 116 3.1 Tangent Lines and the Derivative at a Point 116 3.2 The Derivative as a Function 120 3.3 Differentiation Rules 129 3.4 The Derivative as a Rate of Change 139 3.5 Derivatives of Trigonometric Functions 148 3.6 The Chain Rule 154 3.7 Implicit Differentiation 162 3.8 Derivatives of Inverse Functions and Logarithms 167 3.9 Inverse Trigonometric Functions 177 3.10 Related Rates 184 3.11 Linearization and Differentials 192 Questions to Guide Your Review 203 Practice Exercises 204 Additional and Advanced Exercises 208 iii A01_HASS5540_15_SE_FM.indd 3 03/11/2018 05:24 iv Contents 4 Applications of Derivatives 212 4.1 Extreme Values of Functions on Closed Intervals 212 4.2 The Mean Value Theorem 220 4.3 Monotonic Functions and the First Derivative Test 228 4.4 Concavity and Curve Sketching 233 4.5 Indeterminate Forms and L’Hôpital’s Rule 246 4.6 Applied Optimization 255 4.7 Newton’s Method 266 4.8 Antiderivatives 271 Questions to Guide Your Review 281 Practice Exercises 282 Additional and Advanced Exercises 286 5 Integrals 290 5.1 Area and Estimating with Finite Sums 290 5.2 Sigma Notation and Limits of Finite Sums 300 5.3 The Definite Integral 307 5.4 The Fundamental Theorem of Calculus 320 5.5 Indefinite Integrals and the Substitution Method 332 5.6 Definite Integral Substitutions and the Area Between Curves 339 Questions to Guide Your Review 349 Practice Exercises 350 Additional and Advanced Exercises 353 6 Applications of Definite Integrals 356 6.1 Volumes Using Cross-Sections 356 6.2 Volumes Using Cylindrical Shells 367 6.3 Arc Length 375 6.4 Areas of Surfaces of Revolution 381 6.5 Work 386 6.6 Moments and Centers of Mass 392 Questions to Guide Your Review 401 Practice Exercises 402 Additional and Advanced Exercises 403 7 Integrals and Transcendental Functions 405 7.1 The Logarithm Defined as an Integral 405 7.2 Exponential Change and Separable Differential Equations 415 7.3 Hyperbolic Functions 425 Questions to Guide Your Review 433 Practice Exercises 433 Additional and Advanced Exercises 434 Also available: B.1 Relative Rates of Growth A01_HASS5540_15_SE_FM.indd 4 03/11/2018 05:24 Contents v 8 Techniques of Integration 436 8.1 Integration by Parts 437 8.2 Trigonometric Integrals 445 8.3 Trigonometric Substitutions 451 8.4 Integration of Rational Functions by Partial Fractions 456 8.5 Integral Tables and Computer Algebra Systems 463 8.6 Numerical Integration 469 8.7 Improper Integrals 478 Questions to Guide Your Review 489 Practice Exercises 490 Additional and Advanced Exercises 492 Also available: B.2 Probability 9 Infinite Sequences and Series 495 9.1 Sequences 495 9.2 Infinite Series 508 9.3 The Integral Test 518 9.4 Comparison Tests 524 9.5 Absolute Convergence; The Ratio and Root Tests 529 9.6 Alternating Series and Conditional Convergence 536 9.7 Power Series 543 9.8 Taylor and Maclaurin Series 554 9.9 Convergence of Taylor Series 559 9.10 Applications of Taylor Series 565 Questions to Guide Your Review 574 Practice Exercises 575 Additional and Advanced Exercises 577 Also available: A.6 Commonly Occurring Limits 10 Parametric Equations and Polar Coordinates 580 10.1 Parametrizations of Plane Curves 580 10.2 Calculus with Parametric Curves 588 10.3 Polar Coordinates 598 10.4 Graphing Polar Coordinate Equations 602 10.5 Areas and Lengths in Polar Coordinates 606 Questions to Guide Your Review 611 Practice Exercises 611 Additional and Advanced Exercises 613 Also available: A.4 Conic Sections, B.3 Conics in Polar Coordinates A01_HASS5540_15_SE_FM.indd 5 03/11/2018 05:24 vi Contents 11 Vectors and the Geometry of Space 614 11.1 Three-Dimensional Coordinate Systems 614 11.2 Vectors 619 11.3 The Dot Product 628 11.4 The Cross Product 636 11.5 Lines and Planes in Space 642 11.6 Cylinders and Quadric Surfaces 651 Questions to Guide Your Review 657 Practice Exercises 657 Additional and Advanced Exercises 659 Also available: A.9 The Distributive Law for Vector Cross Products 12 Vector-Valued Functions and Motion in Space 662 12.1 Curves in Space and Their Tangents 662 12.2 Integrals of Vector Functions; Projectile Motion 671 12.3 Arc Length in Space 678 12.4 Curvature and Normal Vectors of a Curve 682 12.5 Tangential and Normal Components of Acceleration 687 12.6 Velocity and Acceleration in Polar Coordinates 690 Questions to Guide Your Review 694 Practice Exercises 694 Additional and Advanced Exercises 696 13 Partial Derivatives 697 13.1 Functions of Several Variables 697 13.2 Limits and Continuity in Higher Dimensions 705 13.3 Partial Derivatives 714 13.4 The Chain Rule 726 13.5 Directional Derivatives and Gradient Vectors 736 13.6 Tangent Planes and Differentials 744 13.7 Extreme Values and Saddle Points 754 13.8 Lagrange Multipliers 763 Questions to Guide Your Review 773 Practice Exercises 773 Additional and Advanced Exercises 777 Also available: A.10 The Mixed Derivative Theorem and the Increment Theorem, B.4 Taylor’s Formula for Two Variables, B.5 Partial Derivatives with Constrained Variables A01_HASS5540_15_SE_FM.indd 6 03/11/2018 05:24 Contents vii 14 Multiple Integrals 779 14.1 Double and Iterated Integrals over Rectangles 779 14.2 Double Integrals over General Regions 784 14.3 Area by Double Integration 793 14.4 Double Integrals in Polar Form 796 14.5 Triple Integrals in Rectangular Coordinates 803 14.6 Applications 813 14.7 Triple Integrals in Cylindrical and Spherical Coordinates 820 14.8 Substitutions in Multiple Integrals 832 Questions to Guide Your Review 841 Practice Exercises 842 Additional and Advanced Exercises 844 15 Integrals and Vector Fields 847 15.1 Line Integrals of Scalar Functions 847 15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux 854 15.3 Path Independence, Conservative Fields, and Potential Functions 867 15.4 Green’s Theorem in the Plane 878 15.5 Surfaces and Area 890 15.6 Surface Integrals 900 15.7 Stokes’ Theorem 910 15.8 The Divergence Theorem and a Unified Theory 923 Questions to Guide Your Review 934 Practice Exercises 934 Additional and Advanced Exercises 937 16 First-Order Differential Equations 16-1 (Online at bit.ly/2pzYlEq) 16.1 Solutions, Slope Fields, and Euler’s Method 16-1 16.2 First-Order Linear Equations 16-9 16.3 Applications 16-15 16.4 Graphical Solutions of Autonomous Equations 16-21 16.5 Systems of Equations and Phase Planes 16-28 Questions to Guide Your Review 16-34 Practice Exercises 16-34 Additional and Advanced Exercises 16-36 17 Second-Order Differential Equations 17-1 (Online at bit.ly/2IHCJyE) 17.1 Second-Order Linear Equations 17-1 17.2 Nonhomogeneous Linear Equations 17-7 17.3 Applications 17-15 17.4 Euler Equations 17-22 17.5 Power-Series Solutions 17-24 A01_HASS5540_15_SE_FM.indd 7 03/11/2018 05:24
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