1 Functions and Models
1.1 Four Ways to Represent a Function
Exercise 4
Exercise 11
Exercise 13
Exercise 17
Exercise 27
Exercise 35
Exercise 45
Exercise 49
Exercise 53
Exercise 61
Exercise 67
1.2 Mathematical Models: A Catalog of Essential Functions
Exercise 3
Exercise 5
Exercise 15
Exercise 17
1.3 New Functions from Old Functions
Exercise 1a
Exercise 1d
Exercise 1h
Exercise 5a
Exercise 5d
Exercise 7
Exercise 15
Exercise 27a
Exercise 27c
Exercise 29a
Exercise 35a
Exercise 35d
Exercise 46
Exercise 53
Exercise 63
1.4 Graphing Calculators and Computers
Exercise 8
Exercise 9
Exercise 25
Exercise 29
Exercise 31
Exercise 35
1.5 Exponential Functions
Exercise 9
Exercise 13
Exercise 15
Exercise 17
Exercise 21
Exercise 27
1.6 Inverse Functions and Logarithms
Exercise 3
Exercise 6
Exercise 13
Exercise 17
Exercise 19
Exercise 22
Exercise 25
Exercise 45
Exercise 47
Exercise 53a
Exercise 53b
Exercise 71
2 Limits and Derivatives
2.1 The Tangent and Velocity Problems
Exercise 3
Exercise 5
Exercise 9
2.2 The Limit of a Function
Exercise 5
Exercise 13
Exercise 17
Exercise 31
Exercise 41
Exercise 48
2.3 Calculating Limits Using the Limit Laws
Exercise 6
Exercise 15
Exercise 18
Exercise 19
Exercise 37
Exercise 41
Exercise 51
Exercise 60
Exercise 63
2.4 The Precise Definition of a Limit
Exercise 3
Exercise 17
Exercise 25
Exercise 29
Exercise 31
Exercise 37
Exercise 43
2.5 Continuity
Exercise 3
Exercise 9
Exercise 13
Exercise 20
Exercise 33
Exercise 36
Exercise 43
Exercise 45
Exercise 51
Exercise 57
Exercise 65
2.6 Limits at Infinity; Horizontal Asymptotes
Exercise 2
Exercise 7
Exercise 19
Exercise 25
Exercise 33
Exercise 43
Exercise 59
Exercise 61
Exercise 69a
Exercise 69b
2.7 Derivatives and Rates of Change
Exercise 7
Exercise 9
Exercise 13
Exercise 17
Exercise 20
Exercise 21
Exercise 25
Exercise 29
Exercise 37
Exercise 41
Exercise 45
Exercise 47
Exercise 53
2.8 The Derivative as a Function
Exercise 3b
Exercise 3c
Exercise 5
Exercise 11
Exercise 19a
Exercise 19b
Exercise 29
Exercise 35
Exercise 37
Exercise 43
Exercise 49
Exercise 53
Exercise 55
3 Differentiation Rules
3.1 Derivatives of Polynomials and Exponential Functions
Exercise 23
Exercise 31
Exercise 35
Exercise 44
Exercise 47
Exercise 51
Exercise 59
Exercise 73
Exercise 77
3.2 The Product and Quotient Rules
Exercise 11
Exercise 25
Exercise 32
Exercise 33
Exercise 36
Exercise 43
Exercise 45
Exercise 52
Exercise 53
Exercise 59
3.3 Derivatives of Trigonometric Functions
Exercise 9
Exercise 22
Exercise 29
Exercise 33
Exercise 37
Exercise 41
Exercise 45
Exercise 49
Exercise 51
Exercise 55
3.4 The Chain Rule
Exercise 5
Exercise 17
Exercise 29
Exercise 37
Exercise 55
Exercise 59
Exercise 61
Exercise 65
Exercise 69
Exercise 77
Exercise 79
Exercise 86
Exercise 95
3.5 Implicit Differentiation
Exercise 15
Exercise 29
Exercise 43
Exercise 51
Exercise 67
Exercise 73
Exercise 77a
Exercise 77b
Exercise 79
3.6 Derivatives of Logarithmic Functions
Exercise 19
Exercise 27
Exercise 43
Exercise 45
Exercise 52
Exercise 55
3.7 Rates of Change in the Natural and Social Sciences
Exercise 1g
Exercise 1h
Exercise 1i
Exercise 15
Exercise 19
Exercise 23
Exercise 30
Exercise 33
Exercise 37
3.8 Exponential Growth and Decay
Exercise 3
Exercise 5
Exercise 9
Exercise 13
Exercise 19
3.9 Related Rates
Exercise 12
Exercise 15
Exercise 19
Exercise 25
Exercise 27
Exercise 33
Exercise 39a
Exercise 39b
Exercise 45
3.10 Linear Approximations and Differentials
Exercise 3
Exercise 5
Exercise 7
Exercise 13
Exercise 15
Exercise 29
Exercise 33
Exercise 40
Exercise 43
3.11 Hyperbolic Functions
Exercise 9
Exercise 15
Exercise 17
Exercise 35
Exercise 43
Exercise 51
Exercise 55
4 Applications of Differentiation
4.1 Maximum and Minimum Values
Exercise 9
Exercise 11
Exercise 13
Exercise 25
Exercise 39
Exercise 41
Exercise 49
Exercise 67
Exercise 78
4.2 The Mean Value Theorem
Exercise 5
Exercise 9
Exercise 19
Exercise 23
Exercise 25
Exercise 35
4.3 How Derivatives Affect the Shape of a Graph
Exercise 5a
Exercise 5b
Exercise 7c
Exercise 11a
Exercise 11b
Exercise 11c
Exercise 17
Exercise 25
Exercise 31
Exercise 39
Exercise 41a
Exercise 41b
Exercise 41c
Exercise 51
Exercise 55
Exercise 63
Exercise 64
Exercise 67
Exercise 77
4.4 Indeterminate Forms and L'Hospital's Rule
Exercise 1
Exercise 25
Exercise 45
Exercise 50
Exercise 57
Exercise 71
Exercise 87
4.5 Summary of Curve Sketching
Exercise 5
Exercise 9
Exercise 19
Exercise 35
Exercise 43
Exercise 61
4.6 Graphing with Calculus and Calculators
Exercise 11
Exercise 13
Exercise 25
Exercise 32
Exercise 33
Exercise 36
4.7 Optimization Problems
Exercise 15
Exercise 18
Exercise 19
Exercise 21
Exercise 24
Exercise 32
Exercise 35
Exercise 51
Exercise 52
Exercise 57b
Exercise 59
Exercise 67
Exercise 73
4.8 Newton's Method
Exercise 4
Exercise 17
Exercise 31
Exercise 37
Exercise 41
4.9 Antiderivatives
Exercise 15
Exercise 23
Exercise 25
Exercise 41
Exercise 51
Exercise 55
Exercise 59
Exercise 67
Exercise 75
5 Integrals
5.1 Areas and Distances
Exercise 2
Exercise 5
Exercise 13
Exercise 17
Exercise 23
5.2 The Definite Integral
Exercise 5
Exercise 9
Exercise 19
Exercise 23
Exercise 33
Exercise 37
Exercise 47
Exercise 49
Exercise 57
5.3 The Fundamental Theorem of Calculus
Exercise 3
Exercise 9
Exercise 13
Exercise 53
Exercise 55
Exercise 66
Exercise 67
Exercise 76
Exercise 77
Exercise 78
5.4 Indefinite Integrals and the Net Change Theorem
Exercise 2
Exercise 9
Exercise 31
Exercise 45
Exercise 50
Exercise 53
Exercise 59
Exercise 61
5.5 The Substitution Rule
Exercise 3
Exercise 13
Exercise 21
Exercise 25
Exercise 35
Exercise 45
Exercise 59
Exercise 64
Exercise 69
Exercise 79
Exercise 85
Exercise 89
6 Applications of Integration
6.1 Areas between Curves
Exercise 3
Exercise 9
Exercise 11
Exercise 13
Exercise 29
Exercise 47
Exercise 53
Exercise 55
6.2 Volumes
Exercise 7
Exercise 9
Exercise 11
Exercise 41
Exercise 47
Exercise 49
Exercise 55
Exercise 61
Exercise 65
6.3 Volumes by Cylindrical Shells
Exercise 5
Exercise 13
Exercise 17
Exercise 25a
Exercise 29
Exercise 41
Exercise 47
6.4 Work
Exercise 7
Exercise 9
Exercise 13
Exercise 17
Exercise 19
Exercise 27
6.5 Average Value of a Function
Exercise 7
Exercise 9
Exercise 13
Exercise 17
Exercise 25
7 Techniques of Integration
7.1 Integration by Parts
Exercise 3
Exercise 15
Exercise 17
Exercise 24
Exercise 39
Exercise 51
Exercise 61
Exercise 67
Exercise 70
7.2 Trigonometric Integrals
Exercise 3
Exercise 7
Exercise 11
Exercise 23
Exercise 29
Exercise 41
Exercise 55
Exercise 61
7.3 Trigonometric Substitution
Exercise 3
Exercise 7
Exercise 13
Exercise 17
Exercise 22
Exercise 31a
Exercise 31b
7.4 Integration of Rational Functions by Partial Fractions
Exercise 6
Exercise 11
Exercise 17
Exercise 23
Exercise 29
Exercise 31
Exercise 43
Exercise 47
Exercise 57
7.5 Strategy for Integration
Exercise 7
Exercise 17
Exercise 23
Exercise 31
Exercise 41
Exercise 45
Exercise 49
Exercise 57
Exercise 63
Exercise 71
7.6 Integration Using Tables and Computer Algebra Systems
Exercise 10
Exercise 17
Exercise 19
Exercise 26
Exercise 29
Exercise 31
Exercise 35
7.7 Approximate Integration
Exercise 1
Exercise 3
Exercise 4
Exercise 35
Exercise 37
Exercise 47
7.8 Improper Integrals
Exercise 1
Exercise 7
Exercise 13
Exercise 21
Exercise 29
Exercise 31
Exercise 49
Exercise 57
Exercise 61
Exercise 69
8 Further Applications of Integration
8.1 Arc Length
Exercise 7
Exercise 11
Exercise 13
Exercise 31
Exercise 33
Exercise 39
Exercise 42
8.2 Area of a Surface of Revolution
Exercise 1a part i
Exercise 1a part ii
Exercise 5
Exercise 11
Exercise 15
Exercise 25
Exercise 31
8.3 Applications to Physics and Engineering
Exercise 7
Exercise 13
Exercise 27
Exercise 31
Exercise 41
8.4 Applications to Economics and Biology
Exercise 5
Exercise 10
Exercise 17
8.5 Probability
Exercise 1
Exercise 7
Exercise 8
Exercise 13
9 Differential Equations
9.1 Modeling with Differential Equations
Exercise 3
Exercise 7
Exercise 9
Exercise 11
Exercise 15
9.2 Direction Fields and Euler's Method
Exercise 3
Exercise 11
Exercise 13
Exercise 18
Exercise 19
Exercise 21
Exercise 23
9.3 Separable Equations
Exercise 10
Exercise 13
Exercise 25
Exercise 31
Exercise 39
Exercise 43
Exercise 49
9.4 Models for Population Growth
Exercise 1
Exercise 3
Exercise 9
Exercise 11
Exercise 16
Exercise 17
Exercise 19
9.5 Linear Equations
Exercise 7
Exercise 9
Exercise 19
Exercise 25
Exercise 31
Exercise 33
9.6 Predator-Prey Systems
Exercise 1
Exercise 5
Exercise 7
Exercise 9
10 Parametric Equations and Polar Coordinates
10.1 Curves Defined by Parametric Equations
Exercise 4
Exercise 9
Exercise 13
Exercise 21
Exercise 31
Exercise 33
Exercise 34
Exercise 41
Exercise 47
Exercise 51
10.2 Calculus with Parametric Curves
Exercise 5
Exercise 11
Exercise 23
Exercise 25
Exercise 31
Exercise 41
Exercise 45
Exercise 63
Exercise 65
10.3 Polar Coordinates
Exercise 11
Exercise 17
Exercise 25
Exercise 33
Exercise 37
Exercise 47
Exercise 53
Exercise 57
Exercise 61
Exercise 65
10.4 Areas and Lengths in Polar Coordinates
Exercise 7
Exercise 21
Exercise 27
Exercise 31
Exercise 41
Exercise 47
10.5 Conic Sections
Exercise 5
Exercise 15
Exercise 19
Exercise 27
Exercise 33
Exercise 37
Exercise 47
10.6 Conic Sections in Polar Coordinates
Exercise 1
Exercise 13
Exercise 13b
Exercise 13c
Exercise 13d
Exercise 21
Exercise 27
(SV AP*) 10 Curves in Parametric, Vector, and Polar Form
(SV AP*) 10.1 Curves Defined by Parametric Equations
Exercise 4
Exercise 9
Exercise 13
Exercise 21
Exercise 31
Exercise 33
Exercise 34
Exercise 41
Exercise 47
Exercise 51
(SV AP*) 10.2 Calculus with Parametric Curves
Exercise 5
Exercise 11
Exercise 23
Exercise 25
Exercise 31
Exercise 41
Exercise 45
Exercise 63
Exercise 65
(SV AP*) 10.3 Vectors in Two Dimensions
Exercise 31
Exercise 45
Exercise 51
(SV AP*) 10.4 Vector Functions and Their Derivatives
Exercise 21
Exercise 31
(SV AP*) 10.5 Curvilinear Motion: Velocity and Acceleration
Exercise 21
(SV AP*) 10.6 Polar Coordinates
Exercise 11
Exercise 17
Exercise 25
Exercise 33
Exercise 37
Exercise 47
Exercise 53
Exercise 57
Exercise 61
Exercise 65
(SV AP*) 10.7 Areas and Lengths in Polar Coordinates
Exercise 7
Exercise 21
Exercise 27
Exercise 31
Exercise 41
Exercise 47
(SV AP*) 10.8 Conic Sections
Exercise 5
Exercise 15
Exercise 19
Exercise 27
Exercise 33
Exercise 37
Exercise 47
(SV AP*) 10.9 Conic Sections in Polar Coordinates
Exercise 1
Exercise 13
Exercise 13b
Exercise 13c
Exercise 13d
Exercise 21
Exercise 27
11 Infinite Sequences and Series
11.1 Sequences
Exercise 17
Exercise 25
Exercise 42
Exercise 43
Exercise 53
Exercise 64
Exercise 71
Exercise 73
Exercise 81
11.2 Series
Exercise 9
Exercise 15
Exercise 23
Exercise 39
Exercise 43
Exercise 51
Exercise 57
Exercise 67
Exercise 73
Exercise 79
Exercise 85
Exercise 87
11.3 The Integral Test and Estimates of Sums
Exercise 7
Exercise 11
Exercise 17
Exercise 21
Exercise 37
Exercise 43
11.4 The Comparison Tests
Exercise 1
Exercise 5
Exercise 7
Exercise 17
Exercise 31
Exercise 37
Exercise 41
11.5 Alternating Series
Exercise 3
Exercise 7
Exercise 11
Exercise 17
Exercise 23
Exercise 32
11.6 Absolute Convergence and the Ratio and Root Tests
Exercise 3
Exercise 13
Exercise 19
Exercise 21
Exercise 31
Exercise 35
Exercise 37
11.8 Power Series
Exercise 5
Exercise 7
Exercise 15
Exercise 23
Exercise 24
Exercise 29
Exercise 37
11.9 Representations of Functions as Power Series
Exercise 5
Exercise 8
Exercise 13a
Exercise 13b
Exercise 15
Exercise 23
Exercise 25
Exercise 37
Exercise 39
11.10 Taylor and Maclaurin Series
Exercise 5
Exercise 15
Exercise 27
Exercise 33
Exercise 35
Exercise 39
Exercise 45
Exercise 57
Exercise 59
Exercise 63
11.11 Applications of Taylor Polynomials
Exercise 5
Exercise 9
Exercise 18
Exercise 19
Exercise 25
Exercise 31
Exercise 33
12 Vectors and the Geometry of Space
12.1 Three-Dimensional Coordinate Systems
Exercise 5
Exercise 13
Exercise 21
Exercise 27
Exercise 33
Exercise 37
Exercise 41
12.2 Vectors
Exercise 3
Exercise 13
Exercise 25
Exercise 29
Exercise 45
Exercise 47
Exercise 51
12.3 The Dot Product
Exercise 11
Exercise 19
Exercise 27
Exercise 45
Exercise 47
Exercise 53
Exercise 55
Exercise 61
12.4 The Cross Product
Exercise 7
Exercise 13
Exercise 16
Exercise 19
Exercise 31
Exercise 45
Exercise 49
Exercise 53
12.5 Equations of Lines and Planes
Exercise 5
Exercise 7
Exercise 13
Exercise 19
Exercise 31
Exercise 51
Exercise 63
Exercise 75
12.6 Cylinders and Quadric Surfaces
Exercise 9
Exercise 19
13 Vector Functions
13.1 Vector Functions and Space Curves
Exercise 13
Exercise 23
Exercise 27
Exercise 41
Exercise 45
13.2 Derivatives and Integrals of Vector Functions
Exercise 1
Exercise 3
Exercise 15
Exercise 19
Exercise 25
Exercise 53
13.3 Arc Length and Curvature
Exercise 3
Exercise 5
Exercise 17
Exercise 31
Exercise 33
Exercise 39
Exercise 47
Exercise 53
Exercise 57
13.4 Motion in Space: Velocity and Acceleration
Exercise 11
Exercise 19
Exercise 22
Exercise 25
Exercise 39
14 Partial Derivatives
14.1 Functions of Several Variables
Exercise 1
Exercise 7
Exercise 15
Exercise 19
Exercise 25
Exercise 32
Exercise 37
Exercise 47
Exercise 59
Exercise 65
Exercise 69
14.2 Limits and Continuity
Exercise 9
Exercise 13
Exercise 21
Exercise 25
Exercise 28
Exercise 37
Exercise 39
14.3 Partial Derivatives
Exercise 1
Exercise 5a
Exercise 5b
Exercise 9
Exercise 21
Exercise 33
Exercise 52
Exercise 73
Exercise 83
Exercise 92
Exercise 93
14.4 Tangent Planes and Linear Approximations
Exercise 11
Exercise 21
Exercise 31
Exercise 35
Exercise 43
Exercise 45
14.5 The Chain Rule
Exercise 5
Exercise 11
Exercise 17
Exercise 35
Exercise 39
Exercise 45
Exercise 47
14.6 Directional Derivatives and the Gradient Vector
Exercise 1
Exercise 11
Exercise 19
Exercise 23
Exercise 27
Exercise 29
Exercise 33
Exercise 41
Exercise 61
Exercise 67
14.7 Maximum and Minimum Values
Exercise 1
Exercise 3
Exercise 13
Exercise 31
Exercise 41
Exercise 43
Exercise 51
14.8 Lagrange Multipliers
Exercise 1
Exercise 3
Exercise 11
Exercise 21
Exercise 27
Exercise 37
Exercise 47
15 Multiple Integrals
15.1 Double Integrals over Rectangles
Exercise 1
Exercise 7
Exercise 9a
Exercise 9b
Exercise 13
Exercise 17
15.2 Iterated Integrals
Exercise 3
Exercise 9
Exercise 17
Exercise 19
Exercise 23
Exercise 27
Exercise 35
15.3 Double Integrals over General Regions
Exercise 5
Exercise 17
Exercise 21
Exercise 25
Exercise 47
Exercise 49
Exercise 55
Exercise 62
15.4 Double Integrals in Polar Coordinates
Exercise 1
Exercise 11
Exercise 13
Exercise 15
Exercise 25
Exercise 39
15.5 Applications of Double Integrals
Exercise 5
Exercise 15
Exercise 27
Exercise 29
15.6 Surface Area
Exercise 3
Exercise 9
Exercise 12
15.7 Triple Integrals
Exercise 13
Exercise 19
Exercise 23
Exercise 27
Exercise 35
Exercise 41
Exercise 53
15.8 Triple Integrals in Cylindrical Coordinates
Exercise 9
Exercise 17
Exercise 21
15.9 Triple Integrals in Spherical Coordinates
Exercise 5
Exercise 17
Exercise 21
Exercise 30
Exercise 35
15.10 Change of Variables in Multiple Integrals
Exercise 7
Exercise 17
Exercise 25
16 Vector Calculus
16.1 Vector Fields
Exercise 5
Exercise 11
Exercise 17
Exercise 23
Exercise 29
Exercise 35
16.2 Line Integrals
Exercise 3
Exercise 7
Exercise 11
Exercise 17
Exercise 21
Exercise 33
Exercise 39
Exercise 45
16.3 The Fundamental Theorem for Line Integrals
Exercise 7
Exercise 11
Exercise 15
Exercise 25
Exercise 29
Exercise 35
16.4 Green's Theorem
Exercise 3
Exercise 7
Exercise 9
Exercise 17
Exercise 21
Exercise 29
16.5 Curl and Divergence
Exercise 11
Exercise 13
Exercise 19
Exercise 21
Exercise 31
16.6 Parametric Surfaces and Their Areas
Exercise 3
Exercise 13
Exercise 19
Exercise 23
Exercise 26
Exercise 33
Exercise 39
Exercise 45
Exercise 49
Exercise 59
Exercise 61
16.7 Surface Integrals
Exercise 4
Exercise 9
Exercise 17
Exercise 23
Exercise 27
Exercise 39
Exercise 47
16.8 Stokes' Theorem
Exercise 1
Exercise 5
Exercise 7
Exercise 15
Exercise 19
16.9 The Divergence Theorem
Exercise 1
Exercise 7
Exercise 19
Exercise 25
17 Second-Order Differential Equations
17.1 Second-Order Linear Equations
Exercise 1
Exercise 9
Exercise 11
Exercise 19
Exercise 31
17.2 Nonhomogeneous Linear Equations
Exercise 5
Exercise 9
Exercise 16
Exercise 18
Exercise 21a
Exercise 21b
Exercise 25
17.3 Applications of Second-Order Differential Equations
Exercise 3
Exercise 9
Exercise 13
Exercise 17
17.4 Series Solutions
Exercise 3
Exercise 9
Appendixes
Appendix G Appendix G
Exercise 1a
Exercise 3
Exercise 5