1 Functions and Limits
1.1 Functions and Their Representations
Exercise 4
Exercise 9
Exercise 11
Exercise 13
Exercise 21
Exercise 29
Exercise 37
Exercise 41
Exercise 45
Exercise 51
Exercise 53
1.2 A Catalog of Essential Functions
Exercise 1
Exercise 5
Exercise 11
Exercise 13
Exercise 17a
Exercise 17d
Exercise 21a
Exercise 21d
Exercise 29
Exercise 37
Exercise 43
Exercise 57
Exercise 65
1.3 The Limit of a Funciton
Exercise 3
Exercise 9
Exercise 23
Exercise 31
Exercise 39
1.4 Calculating Limits
Exercise 6
Exercise 15
Exercise 18
Exercise 19
Exercise 33
Exercise 37
Exercise 45
Exercise 51
Exercise 55
Exercise 63
Exercise 65
1.5 Continuity
Exercise 3
Exercise 9
Exercise 13
Exercise 18
Exercise 28
Exercise 31
Exercise 33
Exercise 39
Exercise 47
1.6 Limits Involving Infinity
Exercise 5
Exercise 15
Exercise 21
Exercise 25
Exercise 35
Exercise 45
Exercise 47
Exercise 53
Exercise 57a
Exercise 57b
2 Derivatives
2.1 Derivatives and Rates of Change
Exercise 5
Exercise 7
Exercise 11
Exercise 15
Exercise 18
Exercise 19
Exercise 23
Exercise 27
Exercise 35
Exercise 37
Exercise 41
Exercise 43
Exercise 49
2.2 The Derivative as a Function
Exercise 3b
Exercise 3c
Exercise 5
Exercise 11
Exercise 17a
Exercise 17b
Exercise 25
Exercise 31
Exercise 33
Exercise 39
Exercise 44
Exercise 47
2.3 Basic Differentiation Rules
Exercise 19
Exercise 32
Exercise 35
Exercise 37
Exercise 43
Exercise 45g
Exercise 45h
Exercise 53
Exercise 59
Exercise 61
Exercise 63
Exercise 69
2.4 The Product and Quotient Rules
Exercise 5
Exercise 19
Exercise 25
Exercise 32
Exercise 35
Exercise 41
Exercise 46
Exercise 47
Exercise 55
2.5 The Chain Rule
Exercise 5
Exercise 17
Exercise 35
Exercise 51
Exercise 53
Exercise 57
Exercise 63
Exercise 70
Exercise 73
2.6 Implicit Differentiation
Exercise 11
Exercise 21
Exercise 33
Exercise 37
Exercise 43
Exercise 49
2.7 Related Rates
Exercise 11
Exercise 15
Exercise 19
Exercise 27
Exercise 33
Exercise 37a
Exercise 37b
Exercise 41
2.8 Linear Approximations and Differentials
Exercise 3
Exercise 5
Exercise 9
Exercise 15
Exercise 17
Exercise 21
Exercise 27
Exercise 29
3 Applications of Differentiation
3.1 Maximum and Minimum Values
Exercise 9
Exercise 11
Exercise 13
Exercise 21
Exercise 31
Exercise 33
Exercise 37
Exercise 49
Exercise 60
3.2 The Mean Value Theorem
Exercise 5
Exercise 9
Exercise 19
Exercise 23
Exercise 25
Exercise 33
3.3 Derivatives and the Shapes of Graphs
Exercise 3a
Exercise 3b
Exercise 3c
Exercise 15
Exercise 19
Exercise 27
Exercise 29a
Exercise 29b
Exercise 29c
Exercise 39
Exercise 44
3.4 Curve Sketching
Exercise 5
Exercise 9
Exercise 17
Exercise 29
Exercise 53
3.5 Optimization Problems
Exercise 11
Exercise 13
Exercise 15
Exercise 17
Exercise 24
Exercise 25
Exercise 27
Exercise 37
Exercise 39
Exercise 43
Exercise 45
Exercise 51
3.6 Newton's Method
Exercise 4
Exercise 18
Exercise 23
Exercise 27
Exercise 29
3.7 Antiderivatives
Exercise 7
Exercise 15
Exercise 17
Exercise 31
Exercise 37
Exercise 39
Exercise 45
Exercise 51
4 Integrals
4.1 Areas and Distances
Exercise 2
Exercise 5
Exercise 9
Exercise 13
Exercise 17
4.2 The Definite Integral
Exercise 7
Exercise 11
Exercise 17
Exercise 21
Exercise 29
Exercise 33
Exercise 39
Exercise 41
Exercise 47
4.3 Evaluating Definite Integrals
Exercise 11
Exercise 29
Exercise 37
Exercise 40
Exercise 45
Exercise 50
Exercise 53
Exercise 59
Exercise 61
4.4 The Fundamental Theorem of Calculus
Exercise 1
Exercise 7
Exercise 9
Exercise 13
Exercise 19
Exercise 25
Exercise 30
Exercise 31
4.5 The Substitution Rule
Exercise 3
Exercise 23
Exercise 47
Exercise 53
Exercise 57
5 Inverse Functions
5.1 Inverse Functions
Exercise 3
Exercise 13
Exercise 17
Exercise 19
Exercise 22
Exercise 39
Exercise 41
5.2 The Natural Logarithmic Function
Exercise 21
Exercise 35
Exercise 39
Exercise 59
Exercise 60
Exercise 73
5.3 The Natural Exponential Function
Exercise 7
Exercise 13
Exercise 25
Exercise 29
Exercise 38
Exercise 39
Exercise 43
Exercise 53
Exercise 55
Exercise 63
Exercise 67
5.4 General Logarithmic and Exponential Functions
Exercise 12
Exercise 17
Exercise 19
Exercise 31
Exercise 33
Exercise 41
Exercise 45
Exercise 48
5.5 Exponential Growth and Decay
Exercise 3
Exercise 5
Exercise 9
Exercise 13
Exercise 19
5.6 Inverse Trigonometric Functions
Exercise 9
Exercise 19
Exercise 33
Exercise 37
Exercise 43
5.7 Hyperbolic Functions
Exercise 9
Exercise 13
Exercise 31
Exercise 39
Exercise 47
Exercise 51
5.8 Indeterminate Forms and l'Hospital's Rule
Exercise 13
Exercise 25
Exercise 30
Exercise 35
Exercise 41
Exercise 55
6 Techniques of Integration
6.1 Integration by Parts
Exercise 3
Exercise 13
Exercise 18
Exercise 29
Exercise 35
Exercise 43
Exercise 46
6.2 Trigonometric Integrals and Substitutions
Exercise 3
Exercise 5
Exercise 9
Exercise 19
Exercise 25
Exercise 41
Exercise 45
Exercise 51
Exercise 55
Exercise 56
6.3 Partial Fractions
Exercise 6
Exercise 11
Exercise 17
Exercise 23
Exercise 27
Exercise 29
Exercise 37
Exercise 39
6.4 Integration with Tables and Computer Algebra Systems
Exercise 6
Exercise 11
Exercise 13
Exercise 17
Exercise 18
Exercise 21
Exercise 23
6.5 Approximate Integration
Exercise 1
Exercise 3
Exercise 4
Exercise 27
Exercise 33
Exercise 39
6.6 Improper Integrals
Exercise 1
Exercise 7
Exercise 13
Exercise 17
Exercise 25
Exercise 29
Exercise 41
Exercise 49
Exercise 51
Exercise 57
7 Applications of Integration
7.1 Areas Between Curves
Exercise 3
Exercise 9
Exercise 11
Exercise 21
Exercise 28
Exercise 35
Exercise 41
7.2 Volumes
Exercise 5
Exercise 7
Exercise 9
Exercise 31
Exercise 33
Exercise 39
Exercise 47
Exercise 51
7.3 Volumes by Cylindrical Shells
Exercise 5
Exercise 13
Exercise 17
Exercise 25
Exercise 29
Exercise 37
Exercise 41
7.4 Arc Length
Exercise 7
Exercise 11
Exercise 13
Exercise 27
Exercise 29
Exercise 35
Exercise 36
7.5 Area of a Surface of Revolution
Exercise 1ai
Exercise 1aii
Exercise 5
Exercise 11
Exercise 15
Exercise 23
7.6 Applications to Physics and Engineering
Exercise 5
Exercise 9
Exercise 13
Exercise 15
Exercise 19
Exercise 29
Exercise 31
Exercise 41
Exercise 45
Exercise 51
7.7 Differential Equations
Exercise 8
Exercise 11
Exercise 19
Exercise 21
Exercise 29
Exercise 31
Exercise 33
Exercise 35
Exercise 39
Exercise 41
Exercise 47
8 Series
8.1 Sequences
Exercise 7
Exercise 11
Exercise 24
Exercise 25
Exercise 29
Exercise 35
Exercise 37
Exercise 43
8.2 Series
Exercise 9
Exercise 11
Exercise 21
Exercise 25
Exercise 31
Exercise 35
Exercise 39
Exercise 45
Exercise 49
Exercise 55
Exercise 57
8.3 The Integral and Comparison Tests
Exercise 3
Exercise 13
Exercise 17
Exercise 19
Exercise 20
Exercise 22
Exercise 29
Exercise 35
Exercise 37
Exercise 39
Exercise 43
8.4 Other Convergence Tests
Exercise 3
Exercise 7
Exercise 9
Exercise 18
Exercise 19
Exercise 27
Exercise 29
Exercise 33
Exercise 43
Exercise 45
8.5 Power Series
Exercise 5
Exercise 7
Exercise 8
Exercise 15
Exercise 19
Exercise 22
Exercise 23
Exercise 31
8.6 Representing Functions as Power Series
Exercise 5
Exercise 8
Exercise 13a
Exercise 13b
Exercise 15
Exercise 23
Exercise 25
Exercise 37
Exercise 39
8.7 Taylor and Maclaurin Series
Exercise 5
Exercise 13
Exercise 25
Exercise 31
Exercise 33
Exercise 37
Exercise 41
Exercise 53
Exercise 55
Exercise 59
8.8 Applications of Taylor Polynomials
Exercise 5
Exercise 7
Exercise 13
Exercise 14
Exercise 19
Exercise 23
Exercise 25
9 Parametric Equations and Polar Coordinates
9.1 Parametric Curves
Exercise 4
Exercise 7
Exercise 11
Exercise 17
Exercise 25
Exercise 27
Exercise 28
Exercise 35
Exercise 39
Exercise 43
9.2 Calculus with Parametric Curves
Exercise 5
Exercise 9
Exercise 19
Exercise 21
Exercise 27
Exercise 37
Exercise 41
9.3 Polar Coordinates
Exercise 11
Exercise 13
Exercise 19
Exercise 27
Exercise 31
Exercise 41
Exercise 49
Exercise 51
Exercise 55
9.4 Areas and Lengths in Polar Coordinates
Exercise 7
Exercise 17
Exercise 21
Exercise 25
Exercise 31
Exercise 35
9.5 Conic Sections in Polar Coordinates
Exercise 1
Exercise 13a
Exercise 13b
Exercise 13c
Exercise 13d
Exercise 19
Exercise 25
10 Vectors and the Geometry of Space
10.1 Three-Dimensional Coordinate Systems
Exercise 5
Exercise 11
Exercise 19
Exercise 25
Exercise 29
Exercise 33
Exercise 35
10.2 Vectors
Exercise 1
Exercise 7
Exercise 17
Exercise 21
Exercise 35
Exercise 37
Exercise 41
10.3 The Dot Product
Exercise 11
Exercise 17
Exercise 23
Exercise 33
Exercise 35
Exercise 41
Exercise 43
Exercise 49
10.4 The Cross Product
Exercise 7
Exercise 13
Exercise 16
Exercise 19
Exercise 31
Exercise 45
Exercise 49
Exercise 53
10.5 Equations of Lines and Planes
Exercise 5
Exercise 7
Exercise 11
Exercise 17
Exercise 25
Exercise 41
Exercise 53
10.6 Cylinders and Quadric Surfaces
Exercise 9
Exercise 19
10.7 Vector Functions and Space Curves
Exercise 11
Exercise 19
Exercise 23
Exercise 29
Exercise 31
Exercise 33
Exercise 43
Exercise 45
Exercise 51
Exercise 81
10.8 Arc Length and Curvature
Exercise 3
Exercise 13
Exercise 27
Exercise 29
Exercise 35
Exercise 39
Exercise 45
Exercise 47
10.9 Motion in Space: Velocity and Acceleration
Exercise 9
Exercise 15
Exercise 18
Exercise 21
Exercise 31
11 Partial Derivatives
11.1 Functions of Several Variables
Exercise 7
Exercise 9
Exercise 13
Exercise 23
Exercise 29
Exercise 41
Exercise 47
Exercise 51
11.2 Limits and Continuity
Exercise 5
Exercise 9
Exercise 15
Exercise 19
Exercise 27
Exercise 29
11.3 Partial Derivatives
Exercise 1
Exercise 3a
Exercise 3b
Exercise 11
Exercise 23
Exercise 44
Exercise 69
Exercise 74
Exercise 75
11.4 Tangent Planes and Linear Approximations
Exercise 11
Exercise 19
Exercise 25
Exercise 29
Exercise 35
Exercise 37
11.5 The Chain Rule
Exercise 3
Exercise 7
Exercise 13
Exercise 26
Exercise 29
Exercise 33
Exercise 37
Exercise 39
11.6 Directional Derivatives and the Gradient Vector
Exercise 7
Exercise 13
Exercise 15
Exercise 19
Exercise 21
Exercise 25
Exercise 31
Exercise 47
Exercise 53
11.7 Maximum and Minimum Values
Exercise 1
Exercise 9
Exercise 25
Exercise 33
Exercise 35
Exercise 43
11.8 Lagrange Multipliers
Exercise 1
Exercise 9
Exercise 19
Exercise 21
Exercise 27
Exercise 37
Exercise 47
12 Multiple Integrals
12.1 Double Integrals over Rectangles
Exercise 1
Exercise 5
Exercise 9
Exercise 11
Exercise 17
Exercise 21
Exercise 23
Exercise 27
Exercise 31
Exercise 39
Exercise 41
12.2 Double Integrals over General Regions
Exercise 5
Exercise 15
Exercise 19
Exercise 23
Exercise 41
Exercise 43
Exercise 49
Exercise 54
12.3 Double Integrals over Polar Coordinates
Exercise 1
Exercise 11
Exercise 17
Exercise 21
Exercise 29
12.4 Applications of Double Integrals
Exercise 5
Exercise 15
12.5 Triple Integrals
Exercise 11
Exercise 17
Exercise 21
Exercise 25
Exercise 33
Exercise 39
Exercise 49
12.6 Triple Integrals in Cylindrical Coordinates
Exercise 9
Exercise 17
Exercise 21
12.7 Triple Integrals in Spherical Coordinates
Exercise 5
Exercise 17
Exercise 21
Exercise 28
Exercise 33
12.8 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 31
13.2 Line Integrals
Exercise 3
Exercise 7
Exercise 11
Exercise 17
Exercise 21
Exercise 31
Exercise 37
Exercise 43
13.3 The Fundamental Theorem for Line Integrals
Exercise 7
Exercise 13
Exercise 21
Exercise 25
Exercise 31
13.4 Green's Theorem
Exercise 3
Exercise 7
Exercise 9
Exercise 17
Exercise 21
Exercise 29
13.5 Curl and Divergence
Exercise 9
Exercise 11
Exercise 17
Exercise 19
Exercise 29
13.6 Parametric Surfaces and Their Areas
Exercise 1
Exercise 11
Exercise 15
Exercise 19
Exercise 22
Exercise 29
Exercise 33
Exercise 39
Exercise 43
Exercise 53
Exercise 55
13.7 Surface Integrals
Exercise 4
Exercise 9
Exercise 17
Exercise 23
Exercise 27
Exercise 37
Exercise 45
13.8 Stokes' Theorem
Exercise 3
Exercise 5
Exercise 13
Exercise 17
13.9 The Divergence Theorem
Exercise 1
Exercise 7
Exercise 19
Exercise 25
Appendixes
Appendix C The Logarithm Defined as an Integral
Exercise 1a
Exercise 3
Exercise 5