1 Functions and Models
1.1 Four Ways to Represent a Function
Exercise 2
Exercise 4
Exercise 12
Exercise 26
Exercise 30
Exercise 42
Exercise 46
Exercise 59
Exercise 65
1.2 Mathematical Models: A Catalog of Essential Functions
Exercise 3
Exercise 31
Exercise 46
Exercise 48
1.3 New Functions from Old Functions
Exercise 1a
Exercise 1d
Exercise 1h
Exercise 5a
Exercise 5d
Exercise 25
Exercise 35a
Exercise 35c
Exercise 37a
Exercise 43a
Exercise 43d
Exercise 54
Exercise 62
Exercise 72
1.4 Exponential Functions
Exercise 13
Exercise 17
Exercise 19
Exercise 23
Exercise 35
Exercise 44
1.5 Inverse Functions and Logarithms
Exercise 3
Exercise 6
Exercise 13
Exercise 17
Exercise 19
Exercise 22
Exercise 25
Exercise 49
Exercise 82
1.6 Parametric Curves
Exercise 4
Exercise 9
Exercise 13
Exercise 20
Exercise 29
Exercise 31
Exercise 32
Exercise 38
Exercise 43
Exercise 47
2 Limits
2.1 The Tangent and Velocity Problems
Exercise 6
Exercise 9
Exercise 14
2.2 The Limit of a Function
Exercise 4
Exercise 10
Exercise 18
Exercise 36
Exercise 42
2.3 Calculating Limits Using the Limit Laws
Exercise 6
Exercise 18
Exercise 21
Exercise 22
Exercise 41
Exercise 45
Exercise 57
Exercise 68
Exercise 71
2.4 Continuity
Exercise 3
Exercise 12
Exercise 20
Exercise 32
Exercise 34
Exercise 37
Exercise 44
Exercise 46
Exercise 55
Exercise 61
Exercise 70
2.5 Limits Involving Infinity
Exercise 2
Exercise 7
Exercise 17
Exercise 39
Exercise 58
Exercise 76
2.6 Derivatives and Rates of Change
Exercise 8
Exercise 10
Exercise 14
Exercise 19
Exercise 27
Exercise 28
Exercise 34
Exercise 38
Exercise 48
Exercise 54
Exercise 60
Exercise 62
Exercise 66
Exercise 69
2.7 The Derivative as a Function
Exercise 3b
Exercise 3c
Exercise 5
Exercise 11
Exercise 20a
Exercise 20b
Exercise 45
Exercise 53
Exercise 64
Exercise 68
3 Differentiation Rules
3.1 Derivatives of Polynomials and Exponential Functions
Exercise 31
Exercise 37
Exercise 48
Exercise 51
Exercise 60
Exercise 69
Exercise 81
Exercise 91
3.2 The Product and Quotient Rules
Exercise 12
Exercise 26
Exercise 34
Exercise 41
Exercise 48
Exercise 54
Exercise 60
Exercise 62
Exercise 71
3.3 Derivatives of Trigonometric Functions
Exercise 9
Exercise 24
Exercise 32
Exercise 38
Exercise 44
Exercise 46
Exercise 48
Exercise 52
Exercise 54
Exercise 56
3.4 The Chain Rule
Exercise 5
Exercise 37
Exercise 55
Exercise 59
Exercise 62
Exercise 77
Exercise 82
Exercise 90
Exercise 93
Exercise 102
Exercise 107
Exercise 111a
Exercise 111b
Exercise 118
3.5 Implicit Differentiation
Exercise 18
Exercise 35
Exercise 57
Exercise 65
Exercise 71
Exercise 75
3.6 Inverse Trigonometric Functions and their Derivatives
Exercise 11
Exercise 19
Exercise 31
Exercise 39
Exercise 41a
Exercise 41b
3.7 Derivatives of Logarithmic Functions
Exercise 20
Exercise 32
Exercise 46
Exercise 66
Exercise 69
3.8 Rates of Change in the Natural and Social Sciences
Exercise 1g
Exercise 1h
Exercise 1i
Exercise 23
Exercise 30
Exercise 33
Exercise 39
3.9 Linear Approximations and Differentials
Exercise 9
Exercise 24
Exercise 31
Exercise 37
Exercise 39
4 Applications of Differentiation
4.1 Related Rates
Exercise 17
Exercise 20
Exercise 28
Exercise 36
Exercise 44
Exercise 50a
Exercise 50b
Exercise 56
4.2 Maximum and Minimum Values
Exercise 11
Exercise 13
Exercise 24
Exercise 37
Exercise 39
Exercise 47
Exercise 71
Exercise 82
4.3 Derivatives and the Shapes of Curves
Exercise 14
Exercise 16c
Exercise 21a
Exercise 21b
Exercise 21c
Exercise 28
Exercise 43
Exercise 59a
Exercise 59b
Exercise 59c
Exercise 66
Exercise 66d
Exercise 71
Exercise 80
Exercise 84
Exercise 85
Exercise 93
Exercise 100
Exercise 102
Exercise 104
4.4 Graphing with Calculus and Calculators
Exercise 12
Exercise 24
Exercise 26
Exercise 27
Exercise 31
Exercise 32
4.5 Indeterminate Forms and l'Hospital's Rule
Exercise 1
Exercise 28
Exercise 46
Exercise 51
Exercise 60
Exercise 72
Exercise 76
Exercise 78
Exercise 85
Exercise 97
4.6 Optimization Problems
Exercise 18
Exercise 23
Exercise 26
Exercise 30
Exercise 41
Exercise 44
Exercise 61
Exercise 62
Exercise 67
Exercise 69
Exercise 78
Exercise 84
4.7 Newton's Method
Exercise 4
Exercise 41
Exercise 51
4.8 Antiderivatives
Exercise 23
Exercise 44
Exercise 57
Exercise 63
Exercise 72
Exercise 79
5 Integrals
5.1 Areas and Distances
Exercise 2
Exercise 6
Exercise 15
Exercise 19
Exercise 27
5.2 The Definite Integral
Exercise 9
Exercise 43
Exercise 49
Exercise 61
Exercise 63
Exercise 73
5.3 Evaluating Definite Integrals
Exercise 11
Exercise 25
Exercise 36
Exercise 39
Exercise 61
Exercise 66
Exercise 73
Exercise 75
Exercise 92
5.4 The Fundamental Theorem of Calculus
Exercise 3
Exercise 15
Exercise 26
Exercise 37
Exercise 38
5.5 The Substitution Rule
Exercise 4
Exercise 24
Exercise 28
Exercise 40
Exercise 50
Exercise 67
Exercise 71
Exercise 76
Exercise 86
Exercise 95
Exercise 99
5.6 Integration by Parts
Exercise 3
Exercise 16
Exercise 23
Exercise 43
Exercise 55
Exercise 61
Exercise 65
5.7 Additional Techniques of Integration
Exercise 3
Exercise 6
Exercise 13
Exercise 28
Exercise 30
Exercise 45
5.8 Integration Using Tables and Computer Algebra Systems
Exercise 6
Exercise 11
Exercise 13
Exercise 17
Exercise 18
Exercise 21
Exercise 23
5.9 Approximate Integration
Exercise 1
Exercise 29
Exercise 31
Exercise 39
5.10 Improper Integrals
Exercise 16
Exercise 25
Exercise 33
Exercise 55
Exercise 63
Exercise 67
Exercise 75
6 Applications of Integration
6.1 More about Areas
Exercise 3
Exercise 11
Exercise 13
Exercise 57
Exercise 63
Exercise 69
6.2 Volumes
Exercise 8
Exercise 11
Exercise 14
Exercise 60
Exercise 62
Exercise 68
Exercise 74
Exercise 78
6.3 Volumes by Cylindrical Shells
Exercise 5
Exercise 13
Exercise 17
Exercise 25
Exercise 29a
Exercise 41
Exercise 47
6.4 Arc Length
Exercise 18
Exercise 21
Exercise 35
Exercise 40
Exercise 43
6.5 Average Value of a Function
Exercise 9
Exercise 11
Exercise 17
Exercise 23
Exercise 30
6.6 Applications to Physics and Engineering
Exercise 5
Exercise 7
Exercise 11
Exercise 15
Exercise 17
Exercise 25
Exercise 33
Exercise 37
Exercise 47
6.7 Applications to Economics and Biology
Exercise 3
Exercise 5
Exercise 10
Exercise 17
6.8 Probability
Exercise 1
Exercise 10
Exercise 15
7 Differential Equations
7.1 Modeling with Differential Equations
Exercise 4
Exercise 8
Exercise 10
Exercise 12
Exercise 16
7.2 Direction Fields and Euler's Method
Exercise 6
Exercise 14
Exercise 16
Exercise 21
Exercise 22
Exercise 24
Exercise 27
7.3 Separable Equations
Exercise 12
Exercise 17
Exercise 31
Exercise 37
Exercise 47
Exercise 52
Exercise 58
7.4 Exponential Growth and Decay
Exercise 5
Exercise 7
Exercise 12
Exercise 16
Exercise 21
Exercise 24
7.5 The Logistic Equation
Exercise 3
Exercise 13
Exercise 17
Exercise 19
Exercise 23
Exercise 25
7.6 Predator-Prey Systems
Exercise 1
Exercise 5
Exercise 7
Exercise 9
8 Infinite Sequences and Series
8.1 Sequences
Exercise 3
Exercise 11
Exercise 29
Exercise 40
Exercise 55
Exercise 59
Exercise 65
Exercise 67
8.2 Series
Exercise 9
Exercise 15
Exercise 40
Exercise 44
Exercise 52
Exercise 70
Exercise 76
Exercise 82
Exercise 87
Exercise 89
8.3 The Integral and Comparison Tests; Estimating Sums
Exercise 3
Exercise 18
Exercise 22
Exercise 26
Exercise 40
Exercise 49
Exercise 55
Exercise 57
8.4 Other Convergence Tests
Exercise 8
Exercise 16
Exercise 20
Exercise 41
Exercise 43
Exercise 44
Exercise 51
8.5 Power Series
Exercise 20
Exercise 23
Exercise 28
Exercise 34
8.6 Representations of Functions as Power Series
Exercise 6
Exercise 9
Exercise 12a
Exercise 12b
Exercise 14
Exercise 22
Exercise 24
Exercise 41
Exercise 43
8.7 Taylor and Maclaurin Series
Exercise 5
Exercise 27
Exercise 33
Exercise 35
Exercise 39
Exercise 45
Exercise 59
Exercise 63
Exercise 69
8.8 Applications of Taylor Polynomials
Exercise 6
Exercise 12
Exercise 21
Exercise 22
Exercise 27
Exercise 33
Exercise 35
9 Vectors and the Geometry of Space
9.1 Three-Dimensional Coordinate Systems
Exercise 5
Exercise 12
Exercise 22
Exercise 28
Exercise 34
Exercise 40
Exercise 44
9.2 Vectors
Exercise 3
Exercise 10
Exercise 27
Exercise 29
Exercise 47
Exercise 51
Exercise 55
9.3 The Dot Product
Exercise 15
Exercise 23
Exercise 39
Exercise 49
Exercise 51
Exercise 57
Exercise 59
Exercise 65
9.4 The Cross Product
Exercise 1
Exercise 4
Exercise 16
Exercise 30
Exercise 48
Exercise 52
Exercise 56
9.5 Equations of Lines and Planes
Exercise 5
Exercise 7
Exercise 14
Exercise 23
Exercise 35
Exercise 51
Exercise 63
Exercise 75
9.6 Functions and Surfaces
Exercise 1
Exercise 6
Exercise 17
Exercise 29
9.7 Cylindrical and Spherical Coordinates
Exercise 6
Exercise 9
Exercise 18
Exercise 20
Exercise 25
Exercise 37
10 Vector Functions
10.1 Vector Functions and Space Curves
Exercise 19
Exercise 31
Exercise 35
Exercise 51
Exercise 55
10.2 Derivatives and Integrals of Vector Functions
Exercise 1
Exercise 3
Exercise 19
Exercise 23
Exercise 31
Exercise 63
10.3 Arc Length and Curvature
Exercise 3
Exercise 5
Exercise 19
Exercise 35
Exercise 37
Exercise 41
Exercise 49
Exercise 56
Exercise 62
10.4 Motion in Space: Velocity and Acceleration
Exercise 13
Exercise 23
Exercise 26
Exercise 29
Exercise 43
10.5 Parametric Surfaces
Exercise 4
Exercise 15
Exercise 21
Exercise 25
Exercise 28
Exercise 33
11 Partial Derivatives
11.1 Functions of Several Variables
Exercise 1
Exercise 7
Exercise 17
Exercise 29
Exercise 41
Exercise 47
Exercise 51
11.2 Limits and Continuity
Exercise 7
Exercise 18
Exercise 26
Exercise 30
Exercise 33
Exercise 42
Exercise 44
11.3 Partial Derivatives
Exercise 1
Exercise 5a
Exercise 5b
Exercise 9
Exercise 21
Exercise 37
Exercise 62
Exercise 86
Exercise 98
Exercise 103
Exercise 104
11.4 Tangent Planes and Linear Approximations
Exercise 14
Exercise 26
Exercise 38
Exercise 42
Exercise 49
Exercise 55
Exercise 57
11.5 The Chain Rule
Exercise 7
Exercise 16
Exercise 24
Exercise 39
Exercise 44
Exercise 48
Exercise 54
Exercise 56
11.6 Directional Derivatives and the Gradient Vector
Exercise 1
Exercise 15
Exercise 24
Exercise 28
Exercise 33
Exercise 35
Exercise 39
Exercise 51
Exercise 69
Exercise 75
11.7 Maximum and Minimum Values
Exercise 1
Exercise 3
Exercise 20
Exercise 39
Exercise 48
Exercise 50
Exercise 58
11.8 Lagrange Multipliers
Exercise 1
Exercise 3
Exercise 15
Exercise 25
Exercise 31
Exercise 40
Exercise 50
12 Multiple Integrals
12.1 Double Integrals over Rectangles
Exercise 1
Exercise 9
Exercise 11a
Exercise 11b
Exercise 15
Exercise 20
12.2 Iterated Integrals
Exercise 5
Exercise 11
Exercise 21
Exercise 23
Exercise 29
Exercise 34
Exercise 42
12.3 Double Integrals over General Regions
Exercise 7
Exercise 21
Exercise 25
Exercise 29
Exercise 53
Exercise 55
Exercise 61
Exercise 68
12.4 Double Integrals in Polar Coordinates
Exercise 1
Exercise 13
Exercise 15
Exercise 18
Exercise 28
Exercise 40
12.5 Applications of Double Integrals
Exercise 1
Exercise 5
Exercise 15
Exercise 23
Exercise 25
12.6 Surface Area
Exercise 3
Exercise 7
Exercise 9
Exercise 21
Exercise 27
12.7 Triple Integrals
Exercise 12
Exercise 20
Exercise 24
Exercise 29
Exercise 37
Exercise 41
Exercise 53
12.8 Triple Integrals in Cylindrical and Spherical Coordinates
Exercise 3
Exercise 7
Exercise 11
Exercise 17
Exercise 26
Exercise 31
12.9 Change of Variables in Multiple Integrals
Exercise 9
Exercise 19
Exercise 27
13 Vector Calculus
13.1 Vector Fields
Exercise 7
Exercise 13
Exercise 21
Exercise 28
Exercise 37
Exercise 43
13.2 Line Integrals
Exercise 3
Exercise 7
Exercise 11
Exercise 18
Exercise 22
Exercise 36
Exercise 42
Exercise 46
13.3 The Fundamental Theorem for Line Integrals
Exercise 9
Exercise 13
Exercise 18
Exercise 30
Exercise 34
Exercise 40
13.4 Green's Theorem
Exercise 3
Exercise 7
Exercise 10
Exercise 19
Exercise 23
Exercise 31
13.5 Curl and Divergence
Exercise 1
Exercise 13
Exercise 18
Exercise 23
Exercise 25
Exercise 35
13.6 Surface Integrals
Exercise 4
Exercise 9
Exercise 17
Exercise 21
Exercise 27
Exercise 38
Exercise 46
13.7 Stokes' Theorem
Exercise 1
Exercise 6
Exercise 8
Exercise 16
Exercise 20
13.8 The Divergence Theorem
Exercise 1
Exercise 7
Exercise 20
Exercise 26