1 Functions and Models
1.1 Four Ways to Represent a Function
Exercise 2
Exercise 9
Exercise 11
Exercise 15
Exercise 25
Exercise 33
Exercise 41
Exercise 45
Exercise 49
Exercise 57
Exercise 61
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 51a
Exercise 51b
Exercise 61
1.7 Parametric Curves
Exercise 4
Exercise 7
Exercise 11
Exercise 19
Exercise 29
Exercise 31
Exercise 32
Exercise 39
Exercise 43
Exercise 45
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 4
Exercise 9
Exercise 15
Exercise 27
Exercise 32
2.3 Calculating Limits Using the Limit Laws
Exercise 6
Exercise 13
Exercise 16
Exercise 17
Exercise 29
Exercise 33
Exercise 39
Exercise 47
Exercise 49
2.4 Continuity
Exercise 3
Exercise 9
Exercise 13
Exercise 16
Exercise 23
Exercise 25
Exercise 28
Exercise 33
Exercise 35
Exercise 41
Exercise 47
Exercise 51
2.5 Limits Involving Infinity
Exercise 2
Exercise 7
Exercise 15
Exercise 23
Exercise 27
Exercise 39
Exercise 51
2.6 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 49
Exercise 53
2.7 The Derivative as a Function
Exercise 3b
Exercise 3c
Exercise 5
Exercise 11
Exercise 17a
Exercise 17b
Exercise 25
Exercise 27
Exercise 35
Exercise 41
Exercise 47
Exercise 51
2.8 What Does f' Say about f?
Exercise 5
Exercise 9
Exercise 13
Exercise 14
Exercise 15
Exercise 21
Exercise 29
3 Differentiation Rules
3.1 Derivatives of Polynomials and Exponential Functions
Exercise 19
Exercise 25
Exercise 29
Exercise 42
Exercise 45
Exercise 48
Exercise 49
Exercise 57
Exercise 63
Exercise 69
Exercise 71
3.2 The Product and Quotient Rules
Exercise 9
Exercise 23
Exercise 31
Exercise 34
Exercise 41
Exercise 43
Exercise 48
Exercise 51
Exercise 53
Exercise 57
3.3 Derivatives of Trigonometric Functions
Exercise 9
Exercise 20
Exercise 27
Exercise 31
Exercise 33
Exercise 37
Exercise 39
Exercise 41
Exercise 43
Exercise 45
Exercise 49
3.4 The Chain Rule
Exercise 5
Exercise 19
Exercise 21
Exercise 33
Exercise 45
Exercise 49
Exercise 51
Exercise 55
Exercise 59
Exercise 67
Exercise 69
Exercise 76
Exercise 81
Exercise 85a
Exercise 85b
Exercise 91
3.5 Implicit Differentiation
Exercise 13
Exercise 25
Exercise 39
Exercise 43
Exercise 51
Exercise 55
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 17
Exercise 23
Exercise 29
Exercise 37
Exercise 44
Exercise 47
3.8 Rates of Change in the Natural and Social Sciences
Exercise 1g
Exercise 1h
Exercise 1i
Exercise 21
Exercise 28
Exercise 31
Exercise 35
3.9 Linear Approximations and Differentials
Exercise 13
Exercise 23
Exercise 25
Exercise 27
Exercise 33
Exercise 35
4 Applications of Differentiation
4.1 Related Rates
Exercise 11
Exercise 15
Exercise 19
Exercise 29
Exercise 33
Exercise 37a
Exercise 37b
Exercise 43
4.2 Maximum and Minimum Values
Exercise 9
Exercise 11
Exercise 13
Exercise 21
Exercise 33
Exercise 35
Exercise 43
Exercise 59
Exercise 66
4.3 Derivatives and the Shapes of Curves
Exercise 5c
Exercise 9a
Exercise 9b
Exercise 9c
Exercise 15
Exercise 27
Exercise 29a
Exercise 29b
Exercise 29c
Exercise 39
Exercise 39d
Exercise 43
Exercise 59
Exercise 61
Exercise 63
Exercise 65
4.4 Graphing with Calculus and Calculators
Exercise 11
Exercise 23
Exercise 25
Exercise 26
Exercise 30
Exercise 31
4.5 Indeterminate Forms and l'Hospital's Rule
Exercise 1
Exercise 19
Exercise 31
Exercise 34
Exercise 41
Exercise 51
Exercise 55
Exercise 57
Exercise 63
Exercise 75
4.6 Optimization Problems
Exercise 11
Exercise 13
Exercise 15
Exercise 20
Exercise 23
Exercise 25
Exercise 37
Exercise 39
Exercise 43
Exercise 45
Exercise 51
Exercise 57
4.7 Newton's Method
Exercise 4
Exercise 18
Exercise 25
Exercise 29
Exercise 33
4.8 Antiderivatives
Exercise 11
Exercise 17
Exercise 19
Exercise 31
Exercise 39
Exercise 41
Exercise 45
Exercise 51
Exercise 55
5 Integrals
5.1 Areas and Distances
Exercise 2
Exercise 5
Exercise 11
Exercise 15
Exercise 21
5.2 The Definite Integral
Exercise 5
Exercise 9
Exercise 19
Exercise 23
Exercise 31
Exercise 35
Exercise 41
Exercise 43
Exercise 51
5.3 Evaluating Definite Integrals
Exercise 7
Exercise 13
Exercise 29
Exercise 37
Exercise 40
Exercise 43
Exercise 50
Exercise 53
Exercise 59
Exercise 61
Exercise 74
5.4 The Fundamental Theorem of Calculus
Exercise 3
Exercise 9
Exercise 13
Exercise 17
Exercise 19
Exercise 30
Exercise 31
5.5 The Substitution Rule
Exercise 3
Exercise 13
Exercise 15
Exercise 19
Exercise 25
Exercise 35
Exercise 47
Exercise 52
Exercise 55
Exercise 61
Exercise 67
Exercise 71
5.6 Integration by Parts
Exercise 3
Exercise 13
Exercise 16
Exercise 27
Exercise 39
Exercise 43
Exercise 46
5.7 Additional Techniques of Integration
Exercise 3
Exercise 6
Exercise 11
Exercise 23
Exercise 25
Exercise 35
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 1
Exercise 7
Exercise 13
Exercise 19
Exercise 27
Exercise 31
Exercise 37
Exercise 43
Exercise 51
Exercise 53
Exercise 59
6 Applications of Integration
6.1 More about Areas
Exercise 3
Exercise 9
Exercise 13
Exercise 23
Exercise 33
Exercise 39
Exercise 45
6.2 Volumes
Exercise 5
Exercise 7
Exercise 9
Exercise 25b
Exercise 31
Exercise 33
Exercise 39
Exercise 45
Exercise 49
6.3 Volumes by Cylindrical Shells
Exercise 5
Exercise 11
Exercise 15
Exercise 19
Exercise 23a
Exercise 31
Exercise 37
6.4 Arc Length
Exercise 7
Exercise 9
Exercise 15
Exercise 23
Exercise 25
Exercise 29
Exercise 32
6.5 Average Value of a Function
Exercise 5
Exercise 7
Exercise 11
Exercise 15
Exercise 21
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 7
Exercise 8
Exercise 13
7 Differential Equations
7.1 Modeling with Differential Equations
Exercise 3
Exercise 7
Exercise 9
Exercise 11
Exercise 15
7.2 Direction Fields and Euler's Method
Exercise 3
Exercise 11
Exercise 13
Exercise 18
Exercise 19
Exercise 21
Exercise 23
7.3 Separable Equations
Exercise 10
Exercise 13
Exercise 25
Exercise 31
Exercise 39
Exercise 43
Exercise 49
7.4 Exponential Growth and Decay
Exercise 3
Exercise 5
Exercise 9
Exercise 13
Exercise 19
Exercise 22
7.5 The Logistic Equation
Exercise 1
Exercise 3
Exercise 9
Exercise 11
Exercise 15
Exercise 17
7.6 Predator-Prey Systems
Exercise 1
Exercise 5
Exercise 7
Exercise 9
8 Infinite Sequences and Series
8.1 Sequences
Exercise 3
Exercise 9
Exercise 11
Exercise 25
Exercise 31
Exercise 45
Exercise 49
Exercise 53
Exercise 55
8.2 Series
Exercise 3
Exercise 9
Exercise 17
Exercise 27
Exercise 31
Exercise 37
Exercise 41
Exercise 47
Exercise 53
Exercise 59
Exercise 63
Exercise 65
8.3 The Integral and Comparison Tests; Estimating Sums
Exercise 3
Exercise 13
Exercise 15
Exercise 17
Exercise 20
Exercise 22
Exercise 29
Exercise 33
Exercise 39
Exercise 41
8.4 Other Convergence Tests
Exercise 3
Exercise 7
Exercise 13
Exercise 15
Exercise 21
Exercise 28
Exercise 29
Exercise 35
Exercise 37
Exercise 39
Exercise 41
8.5 Power Series
Exercise 3
Exercise 7
Exercise 13
Exercise 19
Exercise 24
Exercise 25
Exercise 31
8.6 Representations of Functions as Power Series
Exercise 5
Exercise 8
Exercise 11a
Exercise 11b
Exercise 13
Exercise 21
Exercise 23
Exercise 35
Exercise 37
8.7 Taylor and Maclaurin Series
Exercise 5
Exercise 13
Exercise 23
Exercise 29
Exercise 31
Exercise 35
Exercise 41
Exercise 53
Exercise 55
Exercise 59
8.8 Applications of Taylor Polynomials
Exercise 5
Exercise 7
Exercise 15
Exercise 16
Exercise 21
Exercise 27
Exercise 29
9 Vectors and the Geometry of Space
9.1 Three-Dimensional Coordinate Systems
Exercise 5
Exercise 11
Exercise 19
Exercise 25
Exercise 31
Exercise 35
Exercise 39
9.2 Vectors
Exercise 3
Exercise 9
Exercise 21
Exercise 23
Exercise 35
Exercise 39
Exercise 43
9.3 The Dot Product
Exercise 11
Exercise 17
Exercise 25
Exercise 33
Exercise 35
Exercise 41
Exercise 43
Exercise 49
9.4 The Cross Product
Exercise 1
Exercise 4
Exercise 13
Exercise 19
Exercise 23
Exercise 33
Exercise 35
Exercise 39
9.5 Equations of Lines and Planes
Exercise 5
Exercise 7
Exercise 11
Exercise 17
Exercise 25
Exercise 39
Exercise 47
Exercise 59
9.6 Functions and Surfaces
Exercise 1
Exercise 5
Exercise 15
Exercise 25
9.7 Cylindrical and Spherical Coordinates
Exercise 5
Exercise 7
Exercise 13
Exercise 17
Exercise 21
Exercise 33
10 Vector Functions
10.1 Vector Functions and Space Curves
Exercise 11
Exercise 21
Exercise 25
Exercise 37
Exercise 41
10.2 Derivatives and Integrals of Vector Functions
Exercise 1
Exercise 3
Exercise 13
Exercise 17
Exercise 23
Exercise 51
10.3 Arc Length and Curvature
Exercise 3
Exercise 5
Exercise 17
Exercise 31
Exercise 33
Exercise 37
Exercise 45
Exercise 51
Exercise 55
10.4 Motion in Space: Velocity and Acceleration
Exercise 9
Exercise 17
Exercise 20
Exercise 23
Exercise 35
10.5 Parametric Surfaces
Exercise 3
Exercise 13
Exercise 19
Exercise 23
Exercise 26
Exercise 31
11 Partial Derivatives
11.1 Functions of Several Variables
Exercise 1
Exercise 5
Exercise 13
Exercise 23
Exercise 35
Exercise 41
Exercise 45
11.2 Limits and Continuity
Exercise 7
Exercise 11
Exercise 19
Exercise 23
Exercise 26
Exercise 33
Exercise 35
11.3 Partial Derivatives
Exercise 1
Exercise 5a
Exercise 5b
Exercise 9
Exercise 21
Exercise 31
Exercise 50
Exercise 67
Exercise 79
Exercise 84
Exercise 85
11.4 Tangent Planes and Linear Approximations
Exercise 11
Exercise 19
Exercise 29
Exercise 33
Exercise 39
Exercise 45
Exercise 47
11.5 The Chain Rule
Exercise 5
Exercise 11
Exercise 17
Exercise 30
Exercise 33
Exercise 37
Exercise 43
Exercise 45
11.6 Directional Derivatives and the Gradient Vector
Exercise 1
Exercise 11
Exercise 19
Exercise 21
Exercise 25
Exercise 27
Exercise 31
Exercise 43
Exercise 55
Exercise 61
11.7 Maximum and Minimum Values
Exercise 1
Exercise 3
Exercise 11
Exercise 29
Exercise 37
Exercise 39
Exercise 47
11.8 Lagrange Multipliers
Exercise 1
Exercise 3
Exercise 11
Exercise 19
Exercise 25
Exercise 35
Exercise 45
12 Multiple Integrals
12.1 Double Integrals over Rectangles
Exercise 1
Exercise 7
Exercise 9a
Exercise 9b
Exercise 13
Exercise 17
12.2 Iterated Integrals
Exercise 3
Exercise 9
Exercise 17
Exercise 19
Exercise 23
Exercise 27
Exercise 35
12.3 Double Integrals over General Regions
Exercise 5
Exercise 17
Exercise 21
Exercise 25
Exercise 45
Exercise 47
Exercise 53
Exercise 60
12.4 Double Integrals in Polar Coordinates
Exercise 1
Exercise 11
Exercise 13
Exercise 21
Exercise 25
Exercise 35
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 11
Exercise 19
Exercise 23
Exercise 27
Exercise 35
Exercise 39
Exercise 51
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 7
Exercise 17
Exercise 25
13 Vector Calculus
13.1 Vector Fields
Exercise 5
Exercise 11
Exercise 17
Exercise 23
Exercise 29
Exercise 35
13.2 Line Integrals
Exercise 3
Exercise 7
Exercise 11
Exercise 17
Exercise 21
Exercise 33
Exercise 39
Exercise 43
13.3 The Fundamental Theorem for Line Integrals
Exercise 7
Exercise 11
Exercise 15
Exercise 25
Exercise 29
Exercise 35
13.4 Green's Theorem
Exercise 3
Exercise 7
Exercise 9
Exercise 17
Exercise 21
Exercise 29
13.5 Curl and Divergence
Exercise 1
Exercise 11
Exercise 15
Exercise 19
Exercise 21
Exercise 31
13.6 Surface Integrals
Exercise 4
Exercise 9
Exercise 17
Exercise 21
Exercise 27
Exercise 37
Exercise 45
13.7 Stokes' Theorem
Exercise 1
Exercise 5
Exercise 7
Exercise 15
Exercise 19
13.8 The Divergence Theorem
Exercise 1
Exercise 7
Exercise 19
Exercise 25
Appendixes
Appendix D Precise Definitions of Limits
Exercise 3
Exercise 15
Exercise 19a
Appendix G Integration of Rational Functions by Partial Fractions
Exercise 5
Exercise 11
Exercise 17
Exercise 23
Exercise 27
Exercise 29
Exercise 37
Appendix H.1 Curves in Polar Coordinates
Exercise 11
Exercise 13
Exercise 19
Exercise 29
Exercise 33
Exercise 43
Exercise 47
Exercise 49
Exercise 53
Exercise 57
Appendix H.2 Area and Lengths in Polar Coordinates
Exercise 7
Exercise 9
Exercise 17
Exercise 21
Exercise 25
Exercise 31
Exercise 37