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FIFTH EDITION
MULTIVARIABLE
WITH ANALYTIC GEOMETRY
Henry Edwards
G.
The University of Georgia, Athens
David Penney
E.
The University of Georgia, Athens
=^=
Prentice Hall
=<^F Upper Saddle River, NJ 07458
Digitized by the Internet Archive
2012
in
http://archive.org/details/multivariablecalOOedwa
FIFTH EDITION
LTIVARIABLI
WITH ANALYTIC GEOMETRY
Henry Edwards
G.
The University of Georgia, Athens
David Penney
E.
The University of Georgia, Athens
Prentice Hall
3£±E Upper Saddle River. NJ 07458
Library ofCongress Cataloging-in-Publication Data
Edwards.C. H.(Charles Henry)
[Calculus with analytic geometry.Selections]
—
Multivariate calculus/C.H.Edwards.Jr..David E. Penney.
5th ed.
p. cm.
Selectionsfrom: Calculus with analyticgeometry.5th ed. 1998.
Rev.ed.of:Multivariable calculuswith analytic geometry.4th
ed. 1994.
Includes bibliographical references and index.
ISBN 0-13-793084-4 (pbk.)
1. Calculus. 2.Geometry,Analytic. I.Penney.David E.
II.Title.
QA303.E22325 1998
515.84—dc21 97-24166
CIP
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UpperSaddleRiver,NJ07458
All rightsreserved.Nopartofthisbook maybe
reproduced,inanyformbyanymeans,without
permission inwritingfromthepublisher.
Printedin the UnitedStatesofAmerica
987654321
10
ISBN0-13-793084-4
Prentice-Hall International(UK) Limited.London
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CON
N
T
ABOUT THE AUTHORS
XI
PREFACE •••
XIII
CHAPTER FUNCTIONS AND GRAPHS
1 1
1.1 Functions and Mathematical Modeling '.
A
Square Wading Pool 11
1.2 Graphs of Equations and Functions 12
A
BrokenTree 23
A
1.3 Brief Catalog ofFunctions, Part 1 24
A
Leaning Ladder 33
A
1.4 Brief Catalog of Functions, Part 2 33
A
Spherical Asteroid 44
1.5 What Is Calculus? 45
Definitions and Concepts 48
CHAPTER 2 PRELUDE TO CALCULUS 53
2.1 Tangent Lines and Slope Predictors 54
V Numerical Slope Investigations 63
TexasInstruments TI-82
2.2 The Limit Concept 63
:Yi = +l/R
fl
:V£= fl+H Slopes and Logarithms 76
:Vj= Vs+l/Vz
:Vh= (Vs-VO/H 2.3 More About Limits 77
:Vs= 2.4 The Concept of Continuity 86
:Vt=
:V?= The BrokenTree Again 95
:Vs=
Definitions, Concepts, Results 96
CHAPTER 3 THE DERIVATIVE 99
3.1 The Derivative and Rates of Change 100
A
City's Population Growth 113
3.2 Basic Differentiation Rules 114
A
Cold Liter ofWater 125
3.3 The Chain Rule 125
3.4 Derivatives ofAlgebraic Functions 133
3.5 Maxima and Minima of Functions on Closed Intervals 141
Zooming in on Zeros of the Derivative 148
3.6 Applied Maximum-Minimum Problems 149
Making a Candy Box with a Lid 162
Power Line Design 163
The shaded contents do not appear in Multivariable Calculus.
VI Contents
3.7 Derivatives ofTrigonometric Functions 163
3.8 Implicit Differentiation and Related Rates 174
3.9 Successive Approximations and Newton's Method 182
PROJECT: How Deep Does a Floating Ball Sink? 193
REVIEW: Formulas, Concepts, Definitions 194
CHAPTER 4 ADDITIONAL APPLICATIONS OF THE DERIVATIVE 199
4.1 Introduction 200
4.2 Increments. Differentials, and Linear Approximation 200
4.3 Increasing and Decreasing Functions and the MeanValueTheorem 208
4.4 The First Derivative Test and Applications 219
y=x+2:
asymptote PROJECT: Constructing a Box at Minimal Cost 228
4.5 Simple Curve Sketching 228
/
(2,5)
(0. II Local minimum PROJECT: Some Exotic Graphs 237
Local maximum 4.6 Higher Derivatives and Concavity 238
)-intercept •- a= I: vertical asymptote PROJECT: Invisible Critical Points and Inflection Points 251
4.7 Curve Sketching and Asymptotes 252
PROJECT: Locating Special Points on Exotic Graphs 263
review: Definitions, Concepts, Results 263
CHAPTER 5 THE INTEGRAL 267
5.1 Introduction 268
5.2 Antiderivatives and Initial Value Problems 268
5.3 Elementary Area Computations 282
5.4 Riemann Sums and the Integral 294
PROJECT: Calculator/Computer Riemann Sums 302
5.5 Evaluation of Integrals 304
5.6 Average Values and the Fundamental Theorem of Calculus 314
5.7 Integration by Substitution 324
5.8 Areas of Plane Regions 332
PROJECT: Approximate Area Calculations 342
5.9 Numerical Integration 343
PROJECT: Approximating In2 and 77 by Numerical Integration 356
review: Definitions, Concepts, Results 358
CHAPTER 6 APPLICATIONS OF THE INTEGRAL 361
6.1 Setting Up Integral Formulas 362
6.2 Volumes by the Method of Cross Sections 369
PROJECT: Approximating Volumes ofSolids of Revolution 380
6.3 Volumes by the Method of Cylindrical Shells 381
PROJECT: Design Your Own Ring! 388
6.4 Arc Length and Surface Area of Revolution 389
PROJECT: ApproximatingArc Length and Surface Area 398
The shaded contents do not appear in Multivariate Calculus.
Contents
VII
6.5 Separable Differential Equations 398
6.6 Force and Work 406
review: Definitions, Concepts, Results 416
CHAPTER 7 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 419
7.1 Exponentials. Logarithms, and Inverse Functions 420
PROJECT: Discovering the Number e forYourself 432
7.2 The Natural Logarithm 432
PROJECT: Discovering the Number e by Numerical Integration 442
7.3 The Exponential Function 442
PROJECT: Discovering the Number e as a Limit 449
7.4 General Exponential and Logarithmic Functions 450
project: Going Where No One Has Gone Before 457
7.5 Natural Growth and Decay 457
PROJECT: The Rule of 72—True or False? 466
*7.6 Linear First-Order Equations and Applications 466
review: Definitions, Concepts, Results 472
CHAPTER 8 FURTHER CALCULUS OF TRANSCENDENTAL FUNCTIONS 475
8.1 Introduction 476
8.2 Inverse Trigonometric Functions 476
1.5 8.3 Indeterminate Forms and THopital's Rule 486
(0; li PROJECT: Graphical Investigation of Indeterminate Forms 492
I
8.4 Additional Indeterminate Forms 493
^
0.5 \ _ sin x 8.5 Hyperbolic Functions and Inverse Hyperbolic Functions 498
\ ^^-^
PROJECT: Your First Sky-Dive 507
review: Definitions and Formulas 508
-0.5
-8-6-4-20246
-I
x CHAPTER 9 TECHNIQUES OF INTEGRATION 511
9.1 Introduction 512
9.2 IntegralTables and Simple Substitutions 512
PROJECT: Comparing Different Answers 516
9.3 Integration by Parts 517
9.4 Trigonometric Integrals 524
9.5 Rational Functions and Partial Fractions 531
PROJECT: Bounded Population Growth 540
9.6 Trigonometric Substitution 541
9.7 Integrals Containing Quadratic Polynomials 546
9.8 Improper Integrals 552
PROJECT: Numerical Approximation of Improper Integrals 560
SUMMARY: 561
["he shaded contents do not appear in Multivariate Calculus.
VIII Contents
CHAPTER POLAR COORDINATES AND PLANE CURVES 567
1
2+2sin 10.1 Analytic Geometry and the Conic Sections 568
10.2 Polar Coordinates 573
Calculator/Computer-Generated Polar Coordinates Graphs 580
10.3 Area Computations in Polar Coordinates 581
10.4 Parametric Curves 586
Calculator/Computer Graphing of Parametric Curves 594
10.5 Integral Computations with Parametric Curves 595
Moon Orbits and Race Tracks 602
10.6 The Parabola 604
10.7 The Ellipse 608
10.8 The Hyperbola 613
Concepts and Definitions 619
CHAPTER 11 INFINITE SERIES 623
Initial heighth 11.1 Introduction 624
Heightrh 11.2 Infinite Sequences 624
Heightr2h Nested Radicals and Continued Fractions 633
11.3 Infinite Series and Convergence 634
Numerical Summation and Geometric Series 644
11.4 Taylor Series andTaylor Polynomials 645
Calculating Logarithms on a Deserted Island 658
11.5 The IntegralTest 659
The Number 7r, Once and For All 666
11.6 Comparison Tests for Positive-Term Series 667
11.7 Alternating Series and Absolute Convergence 673
11.8 Power Series 682
11.9 Power Series Computations 694
CalculatingTrigonometric Functions on a Deserted Island 702
Definitions, Concepts, Results 703
CHAPTER 12 VECTORS, CURVES, AND SURFACES IN SPACE 707
Airplane 12.1 Vectors in the Plane 708
12.2 Rectangular Coordinates and Three-Dimensional Vectors 714
12.3 The Cross Product ofTwo Vectors 725
12.4 Lines and Planes in Space 733
12.5 Curves and Motion in Space 742
yPV Y Does a Pitched Baseball Really Curve? 756
i: M. 12.6 Curvature and Acceleration 757
ES .t,;
12.7 Cylinders and Quadric Surfaces 772
12.8 Cylindrical and Spherical Coordinates 783
Personal Cylindrical and Spherical Plots 790
Definitions, Concepts, Results 791
