SOLUTION MANUAL
All Chapters Included
Student Solutions Manual
for
MULTIVARIABLE CALCULUS
SEVENTH EDITION
v
,ABBREVIATIONS AND SYMBOLS
CD concave
downward
CU concave upward
D the domain of f
FDT First Derivative
Test
HA horizontal
asymptote(s)
I interval of
convergence
I/D Increasing/Decreasing Test
IP inflection point(s)
R radius of
convergence
CAS
VA vertical
asymptote(s)
= indicates the use of a computer algebra system.
H
= indicates the use of l’Hospital’s Rule.
j
= indicates the use of Formula j in the Table of Integrals in the back endpapers.
s
= indicates the use of the substitution {u = sin x, du = cos x dx}.
c
= indicates the use of the substitution {u = cos x, du = − sin x dx}.
, Table Of Content
10 PARAMETRIC EQUATIONS AND POLAR COORDINATES 1
10.1 Curves Defined by Parametric Equations 1
10.2 Calculus with Parametric Curves 7
10.3 Polar Coordinates 13
10.4 Areas and Lengths in Polar Coordinates 20
10.5 Conic Sections 26
10.6 Conic Sections in Polar Coordinates
32 Review
35
Problems Plus 43
11 INFINITE SEQUENCES AND SERIES 45
11.1 Sequences 45
11.2 Series 51
11.3 The Integral Test and Estimates of Sums 59
11.4 The Comparison Tests 62
11.5 Alternating Series 65
11.6 Absolute Convergence and the Ratio and Root Tests 68
11.7 Strategy for Testing Series 72
11.8 Power Series 74
11.9 Representations of Functions as Power Series 78
11.10 Taylor and Maclaurin Series 83
11.11 Applications of Taylor Polynomials 90
Review 97
Problems Plus 105
12 VECTORS AND THE GEOMETRY OF SPACE 111
12.1 Three-Dimensional Coordinate Systems 111
12.2 Vectors 114
12.3 The Dot Product 119
viii CONTENTS
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. vii
, 12.4 The Cross Product 123
12.5 Equations of Lines and Planes 128
12.6 Cylinders and Quadric Surfaces 135
Review 140
Problems Plus 147
13 VECTOR FUNCTIONS 151
13.1 Vector Functions and Space Curves 151
13.2 Derivatives and Integrals of Vector Functions 157
13.3 Arc Length and Curvature161
13.4 Motion in Space: Velocity and Acceleration
168 Review 173
Problems Plus 179
14 PARTIAL DERIVATIVES 183
14.1 Functions of Several Variables 183
14.2 Limits and Continuity 192
14.3 Partial Derivatives 195
14.4 Tangent Planes and Linear Approximations 203
14.5 The Chain Rule 207
14.6 Directional Derivatives and the Gradient Vector 213
14.7 Maximum and Minimum Values 220
14.8 Lagrange Multipliers 229
Review 234
Problems Plus 245
15 MULTIPLE INTEGRALS 247
15.1 Double Integrals over Rectangles 247
15.2 Iterated Integrals 249
15.3 Double Integrals over General Regions 251
15.4 Double Integrals in Polar Coordinates 258
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
All Chapters Included
Student Solutions Manual
for
MULTIVARIABLE CALCULUS
SEVENTH EDITION
v
,ABBREVIATIONS AND SYMBOLS
CD concave
downward
CU concave upward
D the domain of f
FDT First Derivative
Test
HA horizontal
asymptote(s)
I interval of
convergence
I/D Increasing/Decreasing Test
IP inflection point(s)
R radius of
convergence
CAS
VA vertical
asymptote(s)
= indicates the use of a computer algebra system.
H
= indicates the use of l’Hospital’s Rule.
j
= indicates the use of Formula j in the Table of Integrals in the back endpapers.
s
= indicates the use of the substitution {u = sin x, du = cos x dx}.
c
= indicates the use of the substitution {u = cos x, du = − sin x dx}.
, Table Of Content
10 PARAMETRIC EQUATIONS AND POLAR COORDINATES 1
10.1 Curves Defined by Parametric Equations 1
10.2 Calculus with Parametric Curves 7
10.3 Polar Coordinates 13
10.4 Areas and Lengths in Polar Coordinates 20
10.5 Conic Sections 26
10.6 Conic Sections in Polar Coordinates
32 Review
35
Problems Plus 43
11 INFINITE SEQUENCES AND SERIES 45
11.1 Sequences 45
11.2 Series 51
11.3 The Integral Test and Estimates of Sums 59
11.4 The Comparison Tests 62
11.5 Alternating Series 65
11.6 Absolute Convergence and the Ratio and Root Tests 68
11.7 Strategy for Testing Series 72
11.8 Power Series 74
11.9 Representations of Functions as Power Series 78
11.10 Taylor and Maclaurin Series 83
11.11 Applications of Taylor Polynomials 90
Review 97
Problems Plus 105
12 VECTORS AND THE GEOMETRY OF SPACE 111
12.1 Three-Dimensional Coordinate Systems 111
12.2 Vectors 114
12.3 The Dot Product 119
viii CONTENTS
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. vii
, 12.4 The Cross Product 123
12.5 Equations of Lines and Planes 128
12.6 Cylinders and Quadric Surfaces 135
Review 140
Problems Plus 147
13 VECTOR FUNCTIONS 151
13.1 Vector Functions and Space Curves 151
13.2 Derivatives and Integrals of Vector Functions 157
13.3 Arc Length and Curvature161
13.4 Motion in Space: Velocity and Acceleration
168 Review 173
Problems Plus 179
14 PARTIAL DERIVATIVES 183
14.1 Functions of Several Variables 183
14.2 Limits and Continuity 192
14.3 Partial Derivatives 195
14.4 Tangent Planes and Linear Approximations 203
14.5 The Chain Rule 207
14.6 Directional Derivatives and the Gradient Vector 213
14.7 Maximum and Minimum Values 220
14.8 Lagrange Multipliers 229
Review 234
Problems Plus 245
15 MULTIPLE INTEGRALS 247
15.1 Double Integrals over Rectangles 247
15.2 Iterated Integrals 249
15.3 Double Integrals over General Regions 251
15.4 Double Integrals in Polar Coordinates 258
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
