Student Solutions Manual Tamas Wiandt Rochester Institute of Technology to accompany CALCULUS Early Transcendentals Single Variable Tenth Edition Howard Anton Drexel University Irl C Bivens Davidson College Stephen L Davis Davidson College John Wiley& Sons, Inc PUBLISHER ACQUISITIONS EDITOR PROJECT EDITOR ASSISTANT CONTENT EDITOR EDITORIAL ASSISTANT CONTENT MANAGER SENIOR PRODUCTION EDITOR SENIOR PHOTO EDITOR COVER DESIGNER COVER PHOTO Laurie Rosatone David Dietz Ellen Keohane Beth Pearson Jacqueline Sinacori Karoline Luciano Kerry Weinstein Sheena Goldstein Madelyn Lesure © David Henderson/Getty Images Founded in 1807, John Wiley & Sons, Inc has been a valued source of knowledge and understanding for more than 200 years, helping people around the world meet their needs and fulfill their aspirations Our company is built on a foundation of principles that include responsibility to the communities we serve and where we live and work In 2008, we launched a Corporate Citizenship Initiative, a global effort to address the environmental, social, economic, and ethical challenges we face in our business Among the issues we are addressing are carbon impact, paper specifications and procurement, ethical conduct within our business and among our vendors, and community and charitable support For more information, please visit our website: www.wiley.com/go/citizenship Copyright ¤ 2012 John Wiley & Sons, Inc All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate percopy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923 (Web site: www.copyright.com) Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 070305774, (201) 748-6011, fax (201) 748-6008, or online at: www.wiley.com/go/permissions ISBN 978-1-118-17381-7 Printed in the United States of America 10 Contents Chapter Before Calculus ……… ………………………………………………………………………… …… Chapter Limits and Continuity ……………………………………………………………………………… 21 Chapter The Derivative …………………………………………………………………………………… …….39 Chapter Topics in Differentiation …………………………… ……………………………………… …….59 Chapter The Derivative in Graphing and Applications …………………………………… ……… 81 Chapter Integration ………………………………………………………………………………………… …… 127 Chapter Applications of the Definite Integral in Geometry, Science, and Engineering… 159 Chapter Principles of Integral Evaluation ……………………………………………………………… 189 Chapter Mathematical Modeling with Differential Equations …………………………………… 217 Chapter Infinite Series …………………………………………………………………………………… …… 229 Chapter 10 Parametric and Polar Curves; Conic Sections ……………………………………….…… 255 Appendix A Graphing Functions Using Calculators and Computer Algebra Systems ……… 287 Appendix B Trigonometry Review ……………………………………………………………………………… 293 Appendix C Solving Polynomial Equations …………………………………………………………………… 297 Before Calculus Exercise Set 0.1 (a) −2.9, −2.0, 2.35, 2.9 (b) None (c) y = (d) −1.75 ≤ x ≤ 2.15, x = −3, x = (e) ymax = 2.8 at x = −2.6; ymin = −2.2 at x = 1.2 (a) Yes (b) Yes (a) 1999, $47,700 (c) No (vertical line test fails) (d) No (vertical line test fails) (b) 1993, $41,600 (c) The slope between 2000 and 2001 is steeper than the slope between 2001 and 2002, so the median income was declining more rapidly during the first year of the 2-year period √ 2 2 (a) √ f2(0) = 3(0) − = −2; f2 (2) = 3(2)2 − = 10; f (−2) = 3(−2) − = 10; f (3) = 3(3) − = 25; f ( 2) = 3( 2) − = 4; f (3t) = 3(3t) − = 27t − √ √ (b) f (0) = 2(0) = 0; f (2) = 2(2) = 4; f (−2) = 2(−2) = −4; f (3) = 2(3) = 6; f ( 2) = 2; f (3t) = 1/(3t) for t > and f (3t) = 6t for t ≤ (a) Natural domain: x = Range: y = (b) Natural domain: x = Range: {1, −1} √ √ (c) Natural domain: x ≤ − or x ≥ Range: y ≥ (d) x2 − 2x + = (x − 1)2 + ≥ So G(x) is defined for all x, and is ≥ y ≥ √ = Natural domain: all x Range: (e) Natural domain: sin x = 1, so x = (2n+ 12 )π, n = 0, ±1, ±2, For such x, −1 ≤ sin x < 1, so < 1−sin x ≤ 2, 1 and 1−sin x ≥ Range: y ≥ −4 (f ) Division by occurs for x = For all other x, xx−2 = x + 2, which is nonnegative for x ≥ −2 Natural √ √ domain: [−2, 2) ∪ (2, +∞) The range of x + is [0, +∞) But we must exclude x = 2, for which x + = Range: [0, 2) ∪ (2, +∞) 11 (a) The curve is broken whenever someone is born or someone dies (b) C decreases for eight hours, increases rapidly (but continuously), and then repeats h 13 t Chapter 15 Yes y = 17 Yes y = √ 25 − x2 √ √25 − x , − 25 − x2 , −5 ≤ x ≤ 0