ALL RIGHTS RESERVED. Printed in the United States of America 2 3 4 5 6 7 15 14 13 12 1Brooks/Cole 20 Davis Drive Belmont, CA Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, includingSingapore, the United Kingdom, Australia, Mexico, Brazil, and Japan.

1. Resolucao Do Livro Um Curso De Calculo Volume 1 Pdf Free
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Locate your local office at: w.cengage.com/globalCengage Learning products are represented in Canada by Nelson Education, Ltd.To learn more about Brooks/Cole, visit w.cengage.com/brookscolePurchase any of our products at your local college store or at our preferred online store w.cengagebrain.com e 2012 Cengnge Learning. All Rights Reserved. Mny not be scanned, copied, or duplicated, or posted to a publicly accessible website. In whole or in pan.I llThis Student Solutions Manual contains detailed solutions to selected exercises in the text Multivariable Calculus, Seventh Edition (Chapters 10-17 of Calculus, Seventh.

Edition, andCalculus: Early Transcendentals, Sevent,h Edition) by James Stewart. Specifically, it includes solutions to the odd-numbered exercises in each chapter section, review section, True-False Quiz, and Problems Plus section.

Also included are all solutions to the Concept Check questions.Because of differences between the regular version and the Early Transcendentals version of the text, some references are given in a dual format. In these cases, readers of the Early Transcendentals text should use the references denoted by 'ET.' Each solution is presented in the context of the corresponding section of the text.

In general, solutions to the initial exercises involving a new concept illustrate that concept in more detail; this knowledge is then utilized in subsequent solutions. Thus, while the intermediate steps of a solution are given, you may need to refer back to earlier exercises in the section or prior sections for additional explanation of the concepts involved. Note that, in many cases, different routes to an answer may exist which are equally valid; also, answers can be expressed in different but equivalent forms.

Thus, the goaJ of this manual is not to give the definitive solution to each exercise, but rather to assist you as a student in understanc#ng the concepts of the text and learning how to apply them to the. Chal- lenge of solving a problem.We would like to thank James Stewart for entrusting us with the writing of this manual and offering suggestions and Kathi Townes of TECH-arts for typesetting and producing this manual as well as. 1.2 Series 51 1.3 The Integral Test and Estimates of Sums 59 1.4 The Comparison Tests 621.5 Alternating Series 65 1.6 Absolute Convergence and the Ratio and Root Tests 68 1.7 Strategy for Testing Series 721.8 Power Series 741.9 Representations of Functions as Power Series 78 1.10 Taylor and Maclaurin Series 83 1.1 Applications of Taylor Polynomials 90Review 97Problems Plus 1050 12 VECTQRS AND THE GEOMETRY OF SPACE 112.1 Three-Dimensional Coordinate Systems 112.2 Vectors 114 12.3 The Dot Product 1190 2012 Ccogagc Learning.

AU Rights Rcscn-cd. May not be scanned, or duplicouccJ, or posletl to a publicly website, in whole or in vii viii o CONTENTS12.4 The Cross Product 12312.5 Equations of Lines and Planes 128. 12.6 C,ylinders and Quadric Surfaces 135Review 140Problems Plus 1470 13 VECTOR FUNCTIONS 15113.1 Vector Functions and Space Curves 15113.2 Derivatives and Integrals of Vector Functions 15713.3 Arc Length and Curvature 161 13.4 Motion in Space: Velocity and Acceleration 168 Review 173Problems Plus 1790 14 PARTIAL DERIVATIVES 183 14.1 Functions of Several Variables 183.

14.2 14.3Limits and Continuity Partial Derivatives 192195 14.4 Tangent Planes and Linear. Approximations 203 14.5 The Chain Rule 20714.6 Directional Derivatives and the Gradient Vector 213 14.7 Maximum and Minimum Values 220 14.8 Lagrange Multipliers 229Review 234Problems Plus 2450 15 MULTIPLE INTEGRALS 24715.1 Double Integrals over Rectangles 24715.2 Iterated Integrals 249 15.3 Double Integrals over General Regions 251 15.4 Double Integrals in Polar Coordinates 258Q 2012 Ccngage Learning. All Rights Rcscned. May not be scanned, copied, or dcd. Or posted to a publicly accessible website, in whole or in part.15.6 15.715.8 15.9 15.10Applications of Double Integrals 261'Surface Area 267 Triple Integrals 269Triple Integrals in Cylindrical CoordinatesTriple Integrals in Spherical Coordinates Change ofVariables in Multiple Integrals Review 289Problems Plus 2970 16. VECTOR CALCULUS 30316.1 Vector Fields 303 16.2 Line Integrals 30516.3 The Fundamental Theorem for Line Integrals 310 16.4 Green's Theorem 31316.5 Curl and Divergence -316 16.6 Parametric Surfaces and Their Areas 32116.7 Surface Integrals 328 16.8 Stokes' Theorem 3.

16.9 The Divergence Theorem 335. Review 337Problems Plus 3430 17 SECOND-ORDER DIFFERENTIAL EQUATIONS 34517.1 Second-Order Linear Equations 345 17.2 Nonhomogeneous Linear Equations 34717.3 Applications Of Second-Order Differential Equations 350 17.4 Series Solutions 352 Review 354.

0 A.PPENDIX 359 H Complex Numbers 359CONTENTS D ix 2012 Ccngoge Learning. All Rights Reserved. M:ty not be scanned, copied, or duplicated, or posted ton publicly uct:cssiic website, in whole or in part.10 D PARAMETRIC EQUATIONS AND POLAR COORDINATES10.1 Curves Defined by Parametric Equations1.

X= t2 + t, y = t2 -t, -2 S t S 2 t -2 -1 0 l 2 X 2 0 0 2 6 y 6 2 0 0 23. X = cos2 t, y = 1 -sin t, 0 S t S 7r /2 t 0 7r/6 7r/3 7r/2 X 1 3/4 1/4 0 y 1 1/2 1-1 0.13 0. X = 3 -4t, y = 2 -3t(a) t -1 0 1 2X 7 3 -1 -5 y 5 2 -1 -4(b) X= 3-4t = 4t =-X+ 3 = t =-+SO y = 2-3t = 2-x + = 2 +X-= y =X-1. X = 1-e, v = t-2, -2 s t s 2(a) t -2 -1 0 1 2X -3 0 1 0 -3 y -4 -3 -2 -1 0(b) y = t-2 = t = y + 2, SO X= 1-t2 = 1-(y + 2? = x = -(y + 2)2 + 1, or x -y2-4y -e 3, with -4 S y S 0 y y(-3, 0) t=2 r=JI. 6(-5, -4) 1=2(7, S) t=-1(3, 2) t=O© 2012 Cegagc Learning. Ail Rights Reserved.

May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in '.hole or in(1, -2) t=O2 D CHAPTER 10 PARAMETRIC EQUATIONS AND POLAR COORDINATES9. X = Vt, y = 1 -t(a) t 0 1 2 3 4 y 1 0 -1 -2.:3X 0 1 1.414 1.732 2(b) x = Vt = t = x2 = y = 1-t = 1-x2. Since t 0, x 0.So the curve is the right half of the parabola y = 1 -x2.1. (a) x =sin y =cos -1r 1r.x2 + y2 = sin2 + cos2 = 1. For -1r 0 0, we have-1 x 0 and 0 y 1. The graph is a semicircle.smt x13.

Resolucao Do Livro Um Curso De Calculo Volume 1 Pdf Free

(a) x = sint, y = csct, 0 1. Thus, the curve is the. (a) x = X1 + (x2-x1)t, y = YI + (y2-Y1)t, 0 5 t 51. Clearly the curve passes through P1(X1, Yl) when t = 0 and through P2(x2, y2) when t = 1. We get the entire curve y = x213 traversed in a left to right direction. Since x = t6 2': 0, we only get the right half of the.x=y = 1(c) x =e-st = (e-t)3 so e-t = xl/3, y = e-2t = (e-t)2 =.(xl/3)2 = x2/3.If t 0, then x andy are between 0 and 1.

Resolucao Do Livro Um Curso De Calculo Volume 1 Pdf India

Since x 0 and y 0, the curve never quite reaches the origin.39.