Ron Larson Calculus, 10e

【实例简介】
Welcome to Calculus, Tenth Edition. We are proud to present this new edition to you. As with all editions, we have been able to incorporate many useful comments from you, our user. For this edition, we have introduced some new features and revised others. You will still find what you expect – a peda
DERIVATIVES AND NTEGRALS Basic differentiation rules d d luv=uv'+yu' 1LA 0 [u门=nt-lu' d 7 (u),t≠0 9.In u d x Lt e=eu 11.log, u a=(n a)ue 12. pa =(In a)au d x 0Om5EoLom0 sin l cos u)u Icos u=-(sin u)u 15.tan u]=(sec2uJu dx d delcot ul-=(esc 2 u)u 16.[ w. drlsec u|-(sec u tan u)u CSC L sc u cot uu d d arcsin u- 20.arccos u 21.arctan dx 22. d larccot ul-1+I2 23. arcsec u 24 arcas u dx l|√a2-1 dr sinh u]-(cosh u )u [cosh ul nn ul dr ltanh u]-(sech Loth u=-(csch u)u sech u--(sech u tanh u)u csch u]--(csch u coth u)u 31.sinh 2.[cosh u 2-1 tanh x 34 dr loth L d x csch u]= √1+ Basic Integration Formulas 1. kf(u)du =k f(u)du 2.[f(a)±gm)dh=|f(u)dn±|g(a)dhe 3. du 8.sin u du =-cos u+C 9. cos u du = sin u+C 10. tan u du=-Inlcos ul+C e°1.cotd= In/sin u+C 12. sec u du= In sec u +tan ul+C a 13. esc u du--InI cot u+C 14. sec2 u du- u +C 15. csc2u du=-cotu+C oo 16. sec u tan u du-secu+C d C 17. CSc u cot u du=-cscu+( 18 arcsin -+ o oom 19 arctan -+ c 20 arcsec l√ mzy be spaTe s%ed fiom the eBook ap: cr(s). Cd: bill rerisx F2 tant al any :me I E.Ibsecuen TRIGONOMETRY Definition of the six Trigonometric Functions Right triangle definitions, where(<0<T/2 in 0 opp csc 6 (0,1 hyp COS 0= 0 hyp 120° Adjacent 5n135° tan g- opp a cot 6= l50° ad opP Circular function definitions, where 0 is any angle x (-1,0)x180° 36002x(1,0) /x2 SIn g-y CSC 、1)7x210y 330 225° 270￥ tan H ot d Reciprocal Identities Double-Angle Formulas sin 2u= 2 sin u cos u SIn x sec x tan r- COL X cos 2u= cos2u-sin2u=2 cos2u-1=1-2 sin2 u 2 tan ut cSc n cOS cotx= tan 2u sec x I- tan' u Quotient dentities Power-Reducing Formulas COS x 1-cos 2u tan x sin x cot x in x SIn-l cos r Pythagorean Identities 2 sin2x+ cos2 x=1 cos 2u 1 +tanx- sec2 x tan- u cotx 1+ cos 2u Cofunction dentities Sum-to-Product Formulas x=cos x COs Sin x sn+siny=2sa(“+)o(" CSC x= sec x tan 2-x=cotx sin u -sin v=2 cosl csc x cot tan x COS u CoS v=2 cos/<+ cOS Even/odd Identities cos u- COS V= 2 sin -sinx co Product-to-Sum Formulas tan x sec(-x)=secx cot(-x)=-cot x sin u sin v=Lcos(u-v)-cos(u v)] Sum and difiference formulas cos u cos v= alcos(u -v)+ cos(u+ v) sin(n±y)= SIn L cOS v± cos u Sin v cos(u v)= cos u cos v+ sin u sin v SAncos y sin(u +v)+ sin(u-v) tant±tan tan(m±y)= 1 tan u tan v cos u sin v-ssin(u v)-sin(u-v) mzy be spaTe s%ed fiom the eBook ap: cr(s). Cd: bill rerisx F2 tant al any :me I E.Ibsecuen Copyright 2012 Cengage Learning. All Rights Rcservcd May net be copied, scanned, or dupl calcd. in whole or in part Due to electron rights, some third party eontent may be suppressed iron the cBouk ard/r cHapter(s). Editcrial review has chemed that any suppressed content does not materially affect the oerall learning expenence, Cengage Learn ng reserves the night to remove additional ecntent at any rights restrictions require iL. Calculus 10e Copyright 2012 Cengage Learning. All Rights Rcservcd May net be copied, scanned, or dupl calcd. in whole or in part Due to electron rights, some third party eontent may be suppressed iron the cBouk ard/r cHapter(s). Editcrial review has chemed that any suppressed content does not materially affect the oerall learning expenence, Cengage Learn ng reserves the night to remove additional ecntent at any rights restrictions require iL. 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 editionschangestocurrenteditionsandalternateformatspleasevisitwww.cengage.com/higheredtosearchbyevious ISBN#, author, title or keyword for materials in your areas of interest Copyright 2012 Cengage Learning. All Rights Rcservcd May net be copied, scanned, or dupl calcd. in whole or in part Due to electron rights, some third party eontent may be suppressed iron the cBouk ard/r cHapter(s). Editcrial review has chemed that any suppressed content does not materially affect the oerall learning expenence, Cengage Learn ng reserves the night to remove additional ecntent at any rights restrictions require iL. Calculus 10e Ron larson The Pennsylvania State University The Behrend college Bruce Edwards University of Florida BROOKS/COLE 1 CENGAGE Learning australia· Brazil. Japan· Korea Mexico· Singapore· Spain United Kingdom, United state Copyright 2012 Cengage Learning. All Rights Rcservcd May net be copied, scanned, or dupl calcd. in whole or in part Due to electron rights, some third party eontent may be suppressed iron the cBouk ard/r cHapter(s). Editcrial review has chemed that any suppressed content does not materially affect the oerall learning expenence, Cengage Learn ng reserves the night to remove additional ecntent at any rights restrictions require iL. BROOKS/COLE CENGAGE Learning" Calculus O 2014, 2010, 2006 Brooks/ Cole, Cengage Learning Tenth Edition ALL RIGHTS RESERVED. No part of this work covered by the copyrighT Ron larson herein may be reproduced, trans mitted, stored, or used in any form or by Pub isher liz covello any means graphic, electronic, or mechanical, inc uding but not limited to Senior Development Editor: Carolyn Lewis photocopying, recording, scanning, digitizing, taping, Web distribution. information networks, or information storage and retrieval systems Assislant editor: Liza Neuslaeller except as permitted under Section 107 or 108 of the 197 6 Uniled Stales Editorial Assistant: Stephanie Kreuz Copyright Act, without the prior written permission of the publisher Associate Media Editor: Guanglei Zhang Senior Content Project Manager: Jessica Rasie For product information and technology assistance, contact us at Art Director: Linda May Cengage Learning Customer Sales Support, 1-800-354-9706 Rights Acquisition Specialist: Shalice Shah-Caldwell For permission to use matcrial from this text or product submitallrequestsonlineatwww.cengage.com/permissions. Manufacturing Planner: Doug Bertke Further permissions questions can be emailed to Text/Cover Designer: Larson Texts, Inc permissionrequest@cengage.com. Cover Image: Larson Texts, Inc. Library of Congress Control Number: 2012948320 SBN-13:978-128505709 sBN-10:1285057090 zo Channel Center Street oston. MA O2210 USA Cengage 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 ional cengage. com/regio Cengage Learning products are represented in Canada by Nelson Education. Ltd Foryourcourseandlearningsolutionsvisitwww.cengage.com Purchase any of our products at your local college store or at our preferredonlinestorewww.cengagebrain.com Please visit login cengage. com and log in to access inslruclor-specific resources. Printed in the united states of america 2345671615141312 Copyright 2012 Cengage Learning. All Rights Rcservcd May net be copied, scanned, or dupl calcd. in whole or in part Due to electron rights, some third party eontent may be suppressed iron the cBouk ard/r cHapter(s). Editcrial review has chemed that any suppressed content does not materially affect the oerall learning expenence, Cengage Learn ng reserves the night to remove additional ecntent at any rights restrictions require iL. Contents P DPreparation for Calculus .1 Graphs and Models 2 P2 Linear Models and Rates of Change 10 P3 Functions and Their Graphs 19 P4 Fitting Models to Data 31 Review Exercises 37 P.S. Problem Solving 39 1> Limits and Their Properties 41 1.1 A Preview of calculus 42 1.2 Finding Limits graphically and numerically 48 1.3 Evaluating Limits Analytically 59 1. 4 Continuity and one-Sided Limits 70 15 nfinite limits 8 Section Project: Graphs and limits of Trigonometric Functions 90 Review Exercises 91 P.S. Problem Solving 93 2>Differentiation 95 2.1 The derivative and the Tangent Line problem 96 2.2 Basic Differentiation Rules and Rates of Change 106 2.3 Product and Quotient Rules and Higher-Order Derivatives 118 2. 4 The chain rule 129 2.5 Implicit Differentiation 140 Section Project: Optical illusions 147 2.6 Related Rates 148 Review Exercises 157 P.S. Problem Solving 15 3> Applications of Differentiation 61 3.1 Extrema on an Interval 162 3.2 Rolles theorem and the mean value theorem 170 3.3 Increasing and Decreasing Functions and the first Derivative Test 177 Section Project: Rainbows 186 3.4 Concavity and the Second derivative Test 187 3.5 Limits at Infinity 195 3.6 A Summary of Curve Sketching 206 3.7 Optimization Problems 215 Section Project: Connecticut River 224 3. 8 Newtons Method 225 3.9 Differentials 231 Review Exercises 238 P.S. Problem Solving 241 Copyright 2012 Cengage Learning. All Rights Rcservcd May net be copied, scanned, or dupl calcd. in whole or in part Due to electron rights, some third party eontent may be suppressed iron the cBouk ard/r cHapter(s). Editcrial review has chemed that any suppressed content does not materially affect the oerall learning expenence, Cengage Learn ng reserves the night to remove additional ecntent at any rights restrictions require iL. 【实例截图】
【核心代码】