1 Functions and Limits
1.1 Four Ways to Represent a Function
Exercise 4
Exercise 13
Exercise 17
Exercise 27
Exercise 35
Exercise 53
Exercise 61
Exercise 67
1.2 Mathematical Models: A Catalog of Essential Functions
Exercise 3
Exercise 7
Exercise 17
Exercise 19
1.3 New Functions from Old Functions
Exercise 1a
Exercise 1d
Exercise 1h
Exercise 5a
Exercise 5d
Exercise 7
Exercise 19
Exercise 29a
Exercise 29c
Exercise 31a
Exercise 37a
Exercise 37d
Exercise 48
Exercise 55
Exercise 65
1.4 The Tangent and Velocity Problems
Exercise 3
Exercise 5
Exercise 9
1.5 The Limit of a Function
Exercise 5
Exercise 13
Exercise 17
Exercise 31
Exercise 49
1.6 Calculating Limits Using the Limit Laws
Exercise 6
Exercise 15
Exercise 18
Exercise 19
Exercise 37
Exercise 41
Exercise 53
Exercise 62
Exercise 65
1.7 The Precise Definition of a Limit
Exercise 3
Exercise 17
Exercise 25
Exercise 29
Exercise 31
Exercise 37
Exercise 43
1.8 Continuity
Exercise 3
Exercise 9
Exercise 11
Exercise 20
Exercise 36
Exercise 43
Exercise 45
Exercise 53
Exercise 69
2 Derivatives
2.1 Derivatives and Rates of Change
Exercise 7
Exercise 9
Exercise 13
Exercise 17
Exercise 22
Exercise 23
Exercise 29
Exercise 33
Exercise 41
Exercise 45
Exercise 51
Exercise 53
Exercise 59
2.2 The Derivative as a Function
Exercise 3b
Exercise 3c
Exercise 5
Exercise 11
Exercise 17a
Exercise 17b
Exercise 27
Exercise 39
Exercise 47
Exercise 53
Exercise 57
Exercise 59
2.3 Differentiation Formulas
Exercise 10
Exercise 17
Exercise 27
Exercise 43
Exercise 54
Exercise 55
Exercise 60
Exercise 63
Exercise 69
Exercise 76
Exercise 77
Exercise 85
Exercise 87
Exercise 101
2.4 Derivatives of Trigonometric Functions
Exercise 9
Exercise 29
Exercise 33
Exercise 37
Exercise 41
Exercise 45
Exercise 51
Exercise 53
Exercise 57
2.5 The Chain Rule
Exercise 5
Exercise 17
Exercise 37
Exercise 59
Exercise 61
Exercise 65
Exercise 73
Exercise 75
Exercise 80
Exercise 87
2.6 Implicit Differentiation
Exercise 15
Exercise 29
Exercise 43
Exercise 51
Exercise 57
Exercise 61
2.7 Rates of Change in the Natural and Social Sciences
Exercise 15
Exercise 19
Exercise 23
Exercise 28
Exercise 31
Exercise 35
2.8 Related Rates
Exercise 14
Exercise 17
Exercise 21
Exercise 27
Exercise 29
Exercise 37
Exercise 43a
Exercise 43b
Exercise 49
2.9 Linear Approximations and Differentials
Exercise 3
Exercise 5
Exercise 9
Exercise 13
Exercise 29
Exercise 31
Exercise 38
Exercise 41
3 Applications of Differentiation
3.1 Maximum and Minimum Values
Exercise 7
Exercise 11
Exercise 13
Exercise 25
Exercise 39
Exercise 41
Exercise 47
Exercise 61
Exercise 72
3.2 The Mean Value Theorem
Exercise 9
Exercise 11
Exercise 21
Exercise 25
Exercise 27
Exercise 35
3.3 How Derivatives Affect the Shape of a Graph
Exercise 5a
Exercise 5b
Exercise 7c
Exercise 11a
Exercise 11b
Exercise 11c
Exercise 23
Exercise 31
Exercise 39
Exercise 41a
Exercise 41b
Exercise 41c
Exercise 47
Exercise 57
Exercise 58
Exercise 59
Exercise 67
3.4 Limits at Infinity; Horizontal Asymptotes
Exercise 2
Exercise 13
Exercise 21
Exercise 37
Exercise 57
Exercise 43
Exercise 63
Exercise 69a
Exercise 69b
3.5 Summary of Curve Sketching
Exercise 5
Exercise 9
Exercise 15
Exercise 35
Exercise 45
3.6 Graphing with Calculus and Calculators
Exercise 11
Exercise 23
3.7 Optimization Problems
Exercise 15
Exercise 20
Exercise 21
Exercise 23
Exercise 26
Exercise 34
Exercise 37
Exercise 53
Exercise 54
Exercise 59b
Exercise 61
Exercise 71
3.8 Newton's Method
Exercise 4
Exercise 29
Exercise 35
Exercise 39
3.9 Antiderivatives
Exercise 15
Exercise 21
Exercise 23
Exercise 37
Exercise 45
Exercise 49
Exercise 53
Exercise 61
Exercise 69
4 Integrals
4.1 Areas and Distances
Exercise 2
Exercise 5
Exercise 13
Exercise 17
Exercise 25
4.2 The Definite Integral
Exercise 5
Exercise 9
Exercise 19
Exercise 23
Exercise 33
Exercise 37
Exercise 47
Exercise 49
Exercise 57
4.3 The Fundamental Theorem of Calculus
Exercise 3
Exercise 9
Exercise 13
Exercise 47
Exercise 53
Exercise 64
Exercise 65
Exercise 74
Exercise 75
4.4 Indefinite Integrals and the Net Change Theorem
Exercise 2
Exercise 9
Exercise 41
Exercise 46
Exercise 49
Exercise 55
Exercise 57
Exercise 74
4.5 The Substitution Rule
Exercise 3
Exercise 25
Exercise 44
Exercise 59
Exercise 63
Exercise 67
Exercise 69
Exercise 71
Exercise 75
Exercise 81
5 Applications of Integration
5.1 Areas Between Curves
Exercise 11
Exercise 13
Exercise 33
Exercise 53
Exercise 59
Exercise 61
Exercise 64
5.2 Volumes
Exercise 7
Exercise 9
Exercise 11
Exercise 41
Exercise 47
Exercise 49
Exercise 55
Exercise 63
Exercise 67
5.3 Volumes by Cylindrical Shells
Exercise 13
Exercise 17
Exercise 25a
Exercise 29
Exercise 41
Exercise 47
5.4 Work
Exercise 7
Exercise 9
Exercise 13
Exercise 17
Exercise 21
Exercise 29
5.5 Average Value of a Function
Exercise 7
Exercise 9
Exercise 13
Exercise 17
Exercise 23
6 Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
6.1 Inverse Functions
Exercise 3
Exercise 6
Exercise 15
Exercise 19
Exercise 21
Exercise 24
Exercise 41
Exercise 43
6.2 Exponential Functions and Their Derivatives
Exercise 5
Exercise 9
Exercise 11
Exercise 13
Exercise 17
Exercise 21
Exercise 35
Exercise 45
Exercise 53
Exercise 59
Exercise 73
Exercise 75
Exercise 87
Exercise 93
Exercise 98
6.2* The Natural Logarithmic Function
Exercise 25
Exercise 39
Exercise 47
Exercise 70
Exercise 71
Exercise 89
6.3 Logarithmic Functions
Exercise 23
Exercise 29a
Exercise 29b
Exercise 36
Exercise 41
Exercise 49
Exercise 61
6.3* The Natural Exponential Function
Exercise 7b
Exercise 12
Exercise 19
Exercise 25
Exercise 37
Exercise 47
Exercise 54
Exercise 55
Exercise 61
Exercise 73
Exercise 75
Exercise 85
Exercise 93
Exercise 98
6.4 Derivatives of Logarithmic Functions
Exercise 21
Exercise 31
Exercise 47
Exercise 49
Exercise 56
Exercise 61
Exercise 77
Exercise 93
6.4* General Logarithmic and Exponential Functions
Exercise 12
Exercise 17
Exercise 37
Exercise 49
Exercise 54
6.5 Exponential Growth and Decay
Exercise 3
Exercise 5
Exercise 9
Exercise 15
Exercise 21
6.6 Inverse Trigonometric Functions
Exercise 13
Exercise 25
Exercise 37
Exercise 45
Exercise 47
Exercise 63
6.7 Hyperbolic Functions
Exercise 9
Exercise 15
Exercise 17
Exercise 37
Exercise 43
Exercise 51
Exercise 55
6.8 Indeterminate Forms and l'Hospital's Rule
Exercise 1
Exercise 27
Exercise 47
Exercise 52
Exercise 59
Exercise 73
Exercise 77
Exercise 85
Exercise 101
7 Techniques of Integration
7.1 Integration by Parts
Exercise 3
Exercise 15
Exercise 17
Exercise 24
Exercise 39
Exercise 51
Exercise 61
Exercise 69
Exercise 72
7.2 Trigonometric Integrals
Exercise 3
Exercise 7
Exercise 11
Exercise 23
Exercise 27
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 71
8 Further Applications of Integration
8.1 Arc Length
Exercise 9
Exercise 13
Exercise 15
Exercise 33
Exercise 35
Exercise 43
Exercise 46
8.2 Area of a Surface of Revolution
Exercise 1
Exercise 1
Exercise 7
Exercise 13
Exercise 17
Exercise 27
Exercise 33
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 12
Exercise 21
8.5 Probability
Exercise 1
Exercise 7
Exercise 8
Exercise 15
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 3
Exercise 5
Exercise 11
Exercise 13
Exercise 18
Exercise 19
Exercise 21
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 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
11 Infinite Sequences and Series
11.1 Sequences
Exercise 17
Exercise 23
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 75
Exercise 81
Exercise 87
Exercise 89
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 7
Exercise 13
Exercise 17
Exercise 25
Exercise 39
Exercise 43
Exercise 45
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 11
Exercise 21
Exercise 33
Exercise 39
Exercise 41
Exercise 45
Exercise 51
Exercise 63
Exercise 67
Exercise 73
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 7
Exercise 15
Exercise 23
Exercise 29
Exercise 37
Exercise 41
Exercise 45
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 43
Exercise 47
13.2 Derivatives and Integrals of Vector Functions
Exercise 1
Exercise 3
Exercise 15
Exercise 19
Exercise 25
Exercise 55
13.3 Arc Length and Curvature
Exercise 3
Exercise 5
Exercise 17
Exercise 31
Exercise 33
Exercise 39
Exercise 47
Exercise 53
Exercise 59
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 49
Exercise 61
Exercise 67
Exercise 71
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 96
Exercise 97
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
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 69
14.7 Maximum and Minimum Values
Exercise 1
Exercise 3
Exercise 15
Exercise 33
Exercise 43
Exercise 45
Exercise 53
14.8 Lagrange Multipliers
Exercise 1
Exercise 3
Exercise 11
Exercise 23
Exercise 29
Exercise 37
Exercise 47
15 Multiple Integrals
15.1 Double Integrals over Rectangles
Exercise 1
Exercise 5
Exercise 7a
Exercise 7b
Exercise 11
Exercise 29
Exercise 15
Exercise 21
Exercise 29
Exercise 31
Exercise 35
Exercise 39
Exercise 47
15.2 Double Integrals over General Regions
Exercise 5
Exercise 17
Exercise 21
Exercise 25
Exercise 49
Exercise 51
Exercise 57
Exercise 64
15.3 Double Integrals in Polar Coordinates
Exercise 11
Exercise 13
Exercise 15
Exercise 25
Exercise 39
15.4 Applications of Double Integrals
Exercise 5
Exercise 15
Exercise 27
Exercise 29
15.5 Surface Area
Exercise 3
Exercise 9
Exercise 12
15.6 Triple Integrals
Exercise 13
Exercise 19
Exercise 23
Exercise 27
Exercise 35
Exercise 41
Exercise 53
15.7 Triple Integrals in Cylindrical Coordinates
Exercise 9
Exercise 17
Exercise 21
15.8 Triple Integrals in Spherical Coordinates
Exercise 5
Exercise 17
Exercise 21
Exercise 30
Exercise 35
15.9 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