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Browse Visuals and Modules
1 Functions and Limits
M1.3/1.6 Precise Definitions of Limits
2 Derivatives
V2.1A Secant Line and Tangent
V2.1B Tangent Zoom
V2.2 Slope-a-Scope
M2.2 How do Coefficients Affect Graphs?
V2.3 Slope-a-Scope (Trigonometric)
M2.3 The Dynamics of Linear Motion
3 Applications of Differentiation
M3.4 Using Derivatives to Sketch f
M3.5 Analyzing Optimization Problems
M3.6 Newton's Method
4 Integrals
V4.1 Area Under a Parabola
M4.2/6.5 Estimating Areas under Curves
V4.2 Integral with Riemann Sums
M4.4 Fundamental Theorem of Calculus
5 Inverse Functions
V5.3 Slope-a-Scope (Exponential)
6 Techniques of Integration
M6.6 Improper Integrals
7 Applications of Integration
V7.2A Approximating the Volume
V7.2B Volumes of Revolution
V7.2C A Solid With Triangular Slices
V7.3 Volumes of Revolution
V7.4 Circumference as Limit of Polygons
M7.6 Direction Fields and Solution Curves
8 Series
M8.2 An Unusual Series and Its Sums
M8.7/8.8 Taylor and MacLaurin Series
9 Parametric Equations and Polar Coordinates
M9.1A Parametric Curves
M9.1B Families of Cycloids
M9.3 Polar Curves
10 Vectors and the Geometry of Space
V10.2 Adding Vectors
V10.3A The Dot Product of Two Vectors
V10.3B Vector Projections
V10.4 The Cross Product
M10.6A Traces of a Surface
M10.6B Quadric Surfaces
V10.7A Vector Functions and Space Curves
V10.7B The Twisted Cubic Curve
V10.7C Visualizing Space Curves
V10.8A The Unit Tangent Vector
V10.8B The TNB Frame
V10.8C Osculating Circle
V10.9 Velocity and Acceleration Vectors
11 Partial Derivatives
V11.1A Animated Level Curves
V11.1B Level Curves of a Surface
V11.2 Limit that Does Not Exist
V11.4 The Tangent Plane of a Surface
V11.6A Directional Derivatives
V11.6B Maximizing Directional Derivative
M11.7 Critical Points from Contour Maps
V11.8 Lagrange Multipliers
12 Multiple Integrals
V12.1 Fubini's Theorem
V12.5 Regions of Triple Integrals
M12.7 Surfaces in Cyl. and Sph. Coords
V12.7 Region in Spherical Coordinates
13 Vector Calculus
V13.1 Vector Fields
V13.6 Grid Curves on Parametric Surface
M13.6 Families of Parametric Surfaces
V13.7 A Nonorientable Surface
Browse Homework Hints
1 Functions and Limits
1.1 Functions and Their Representations
Exercise 2
Exercise 7
Exercise 9
Exercise 11
Exercise 19
Exercise 27
Exercise 35
Exercise 39
Exercise 43
Exercise 49
Exercise 51
1.2 A Catalog of Essential Functions
Exercise 1
Exercise 11
Exercise 13
Exercise 15a
Exercise 15d
Exercise 15h
Exercise 19a
Exercise 19d
Exercise 27
Exercise 35
Exercise 41a
Exercise 41d
Exercise 48
Exercise 55
Exercise 65
1.3 The Limit of a Function
Exercise 4
Exercise 9
Exercise 31
Exercise 39
1.4 Calculating Limits
Exercise 6
Exercise 15
Exercise 19
Exercise 29
Exercise 33
Exercise 39
Exercise 45
Exercise 47
Exercise 53
Exercise 55
1.5 Continuity
Exercise 3
Exercise 7
Exercise 11
Exercise 16
Exercise 21
Exercise 26
Exercise 29
Exercise 31
Exercise 37
Exercise 45
1.6 Limits Involving Infinity
Exercise 5
Exercise 15
Exercise 19
Exercise 23
Exercise 33
Exercise 41
Exercise 43
Exercise 49
Exercise 53
2 Derivatives
2.1 Derivatives and Rates of Change
Exercise 3
Exercise 5
Exercise 7
Exercise 11
Exercise 15
Exercise 16
Exercise 17
Exercise 21
Exercise 25
Exercise 33
Exercise 35
Exercise 39
Exercise 41
Exercise 43
Exercise 47
2.2 The Derivative as a Function
Exercise 3b
Exercise 3c
Exercise 5
Exercise 11
Exercise 15a
Exercise 15b
Exercise 21
Exercise 23
Exercise 27
Exercise 33
Exercise 38
Exercise 41
2.3 Basic Differentiation Formulas
Exercise 19
Exercise 27
Exercise 30
Exercise 33
Exercise 35
Exercise 41
Exercise 51
Exercise 53
Exercise 57
Exercise 59
Exercise 61
Exercise 65
2.4 The Product and Quotient Rules
Exercise 5
Exercise 19
Exercise 25
Exercise 32
Exercise 35
Exercise 41
Exercise 46
Exercise 51
Exercise 53
2.5 The Chain Rule
Exercise 5
Exercise 17
Exercise 35
Exercise 47
Exercise 51
Exercise 53
Exercise 57
Exercise 58
Exercise 59
Exercise 64
2.6 Implicit Differentiation
Exercise 11
Exercise 19
Exercise 31
Exercise 35
Exercise 39
Exercise 43
2.7 Related Rates
Exercise 9
Exercise 13
Exercise 17
Exercise 25
Exercise 29
Exercise 33a
Exercise 33b
Exercise 37
2.8 Linear Approximations and Differentials
Exercise 3
Exercise 5
Exercise 9
Exercise 15
Exercise 21
Exercise 25
Exercise 27
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 11
Exercise 19
Exercise 23
Exercise 25
Exercise 33
3.3 Derivatives and the Shapes of Graphs
Exercise 3
Exercise 15
Exercise 19
Exercise 27
Exercise 39
Exercise 41
Exercise 42
3.4 Curve Sketching
Exercise 5
Exercise 9
Exercise 17
Exercise 29
Exercise 51
3.5 Optimization Problems
Exercise 9
Exercise 11
Exercise 13
Exercise 18
Exercise 19
Exercise 21
Exercise 31
Exercise 33
Exercise 37
Exercise 43
Exercise 49
3.6 Newton's Method
Exercise 4
Exercise 18
Exercise 23
Exercise 29
3.7 Antiderivatives
Exercise 7
Exercise 13
Exercise 25
Exercise 31
Exercise 33
Exercise 39
Exercise 45
4 Integrals
4.1 Areas and Distances
Exercise 2
Exercise 5
Exercise 7
Exercise 11
Exercise 15
4.2 The Definite Integral
Exercise 7
Exercise 11
Exercise 17
Exercise 21
Exercise 29
Exercise 33
Exercise 39
Exercise 41
4.3 Evaluating Definite Integrals
Exercise 13
Exercise 35
Exercise 38
Exercise 41
Exercise 46
Exercise 49
Exercise 55
Exercise 57
4.4 The Fundamental Theorem of Calculus
Exercise 1
Exercise 7
Exercise 13
Exercise 19
Exercise 25
Exercise 30
Exercise 31
4.5 The Substitution Rule
Exercise 3
Exercise 23
Exercise 44
Exercise 53
Exercise 57
5 Inverse Functions
5.1 Inverse Functions
Exercise 3
Exercise 8
Exercise 13
Exercise 19
Exercise 22
Exercise 37
Exercise 39
5.2 The Natural Logarithmic Function
Exercise 9
Exercise 19
Exercise 33
Exercise 37
Exercise 60
Exercise 61
Exercise 73
5.3 The Natural Exponential Function
Exercise 7a
Exercise 7b
Exercise 13
Exercise 23
Exercise 27
Exercise 36
Exercise 41
Exercise 50
Exercise 51
Exercise 59
Exercise 63
5.4 General Logarithmic and Exponential Functions
Exercise 12
Exercise 17
Exercise 27
Exercise 33
Exercise 45
Exercise 50
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 31
Exercise 37
5.7 Hyperbolic Functions
Exercise 9
Exercise 13
Exercise 35
Exercise 39
Exercise 43
Exercise 45
5.8 Indeterminate Forms and l'Hospital's Rule
Exercise 13
Exercise 25
Exercise 28
Exercise 33
Exercise 39
Exercise 49
6 Techniques of Integration
6.1 Integration by Parts
Exercise 3
Exercise 13
Exercise 16
Exercise 27
Exercise 33
Exercise 41
Exercise 44
6.2 Trigonometric Integrals and Substitutions
Exercise 3
Exercise 5
Exercise 14
Exercise 19
Exercise 25
Exercise 39
Exercise 43
Exercise 49
Exercise 53
Exercise 54
6.3 Partial Fractions
Exercise 5
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 29
Exercise 37
6.6 Improper Integrals
Exercise 1
Exercise 7
Exercise 13
Exercise 17
Exercise 25
Exercise 29
Exercise 35
Exercise 43
Exercise 49
Exercise 51
Exercise 57
7 Applications of Integration
7.1 Areas between Curves
Exercise 3
Exercise 9
Exercise 11
Exercise 21
Exercise 24
Exercise 31
Exercise 37
7.2 Volumes
Exercise 5
Exercise 7
Exercise 9
Exercise 25
Exercise 27
Exercise 33
Exercise 41
Exercise 45
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 3
Exercise 7
Exercise 9
Exercise 25
Exercise 27
Exercise 31
Exercise 32
7.5 Applications to Physics and Engineering
Exercise 5
Exercise 9
Exercise 13
Exercise 15
Exercise 19
Exercise 25
Exercise 27
Exercise 37
Exercise 41
Exercise 43
Exercise 47
7.6 Differential Equations
Exercise 8
Exercise 9
Exercise 19
Exercise 21
Exercise 29
Exercise 31
Exercise 33
Exercise 35
Exercise 39
Exercise 41
Exercise 47
8 Series
8.1 Sequences
Exercise 5
Exercise 9
Exercise 21
Exercise 25
Exercise 31
Exercise 33
Exercise 39
8.2 Series
Exercise 7
Exercise 17
Exercise 19
Exercise 23
Exercise 27
Exercise 31
Exercise 35
Exercise 39
Exercise 45
Exercise 47
8.3 The Integral and Comparison Tests
Exercise 3
Exercise 11
Exercise 13
Exercise 15
Exercise 16
Exercise 18
Exercise 21
Exercise 25
Exercise 31
Exercise 33
Exercise 35
Exercise 39
8.4 Other Convergence Tests
Exercise 3
Exercise 7
Exercise 11
Exercise 18
Exercise 19
Exercise 24
Exercise 25
Exercise 27
Exercise 33
Exercise 39
Exercise 41
8.5 Power Series
Exercise 3
Exercise 7
Exercise 8
Exercise 13
Exercise 17
Exercise 18
Exercise 19
Exercise 25
8.6 Representing Functions as Power Series
Exercise 6
Exercise 7
Exercise 13a
Exercise 13b
Exercise 15
Exercise 21
Exercise 23
Exercise 35
Exercise 37
8.7 Taylor and Maclaurin Series
Exercise 5
Exercise 13
Exercise 25
Exercise 32
Exercise 33
Exercise 37
Exercise 41
Exercise 53
Exercise 55
Exercise 59
Exercise 67
8.8 Applications of Taylor Polynomials
Exercise 3
Exercise 7
Exercise 13
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 41
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 29
Exercise 33
Exercise 41
Exercise 49
Exercise 51
Exercise 55
9.4 Areas and Lengths in Polar Coordinates
Exercise 7
Exercise 9
Exercise 17
Exercise 21
Exercise 25
Exercise 31
Exercise 35
9.5 Conic Sections in Polar Coordinates
Exercise 3
Exercise 13
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 19
Exercise 21
Exercise 27
Exercise 29
Exercise 33
10.3 The Dot Product
Exercise 9
Exercise 15
Exercise 21
Exercise 27
Exercise 29
Exercise 35
Exercise 37
Exercise 43
10.4 The Cross Product
Exercise 7
Exercise 9
Exercise 12
Exercise 15
Exercise 25
Exercise 27
Exercise 39
Exercise 41
Exercise 45
10.5 Equations of Lines and Planes
Exercise 5
Exercise 7
Exercise 11
Exercise 17
Exercise 25
Exercise 39
Exercise 51
10.6 Cylinders and Quadric Surfaces
Exercise 9
Exercise 19
10.7 Vector Functions and Space Curves
Exercise 11
Exercise 17
Exercise 19
Exercise 23
Exercise 29
Exercise 31
Exercise 33
Exercise 43
Exercise 45
Exercise 51
Exercise 53
Exercise 77
10.8 Arc Length and Curvature
Exercise 3
Exercise 11
Exercise 25
Exercise 27
Exercise 31
Exercise 35
Exercise 41
Exercise 43
10.9 Motion in Space: Velocity and Acceleration
Exercise 9
Exercise 15
Exercise 18
Exercise 21
Exercise 29
11 Partial Derivatives
11.1 Functions of Several Variables
Exercise 7
Exercise 9
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 3
Exercise 11
Exercise 21
Exercise 42
Exercise 65
Exercise 70
Exercise 71
11.4 Tangent Planes and Linear Approximations
Exercise 11
Exercise 17
Exercise 23
Exercise 27
Exercise 33
Exercise 35
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 19
Exercise 21
Exercise 25
Exercise 33
Exercise 43
Exercise 49
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 17
Exercise 19
Exercise 23
Exercise 33
Exercise 43
12 Multiple Integrals
12.1 Double Integrals over Rectangles
Exercise 1
Exercise 5
Exercise 9
Exercise 11
Exercise 17
Exercise 21
Exercise 23
Exercise 29
Exercise 37
Exercise 39
12.2 Double Integrals over General Regions
Exercise 5
Exercise 11
Exercise 15
Exercise 19
Exercise 35
Exercise 37
Exercise 43
Exercise 48
12.3 Double Integrals in Polar Coordinates
Exercise 1
Exercise 11
Exercise 17
Exercise 21
Exercise 29
12.4 Applications of Double Integrals
Exercise 1
Exercise 5
Exercise 13
12.5 Triple Integrals
Exercise 9
Exercise 17
Exercise 21
Exercise 25
Exercise 33
Exercise 37
Exercise 45
12.6 Triple Integrals in Cylindrical Coordinates
Exercise 3
Exercise 17
Exercise 21
12.7 Triple Integrals in Spherical Coordinates
Exercise 1
Exercise 5
Exercise 15
Exercise 17
Exercise 21
Exercise 26
Exercise 31
12.8 Change of Variables in Multiple Integrals
Exercise 2
Exercise 5
Exercise 7
Exercise 13
Exercise 21
13 Vector Calculus
13.1 Vector Fields
Exercise 5
Exercise 11
Exercise 17
Exercise 23
Exercise 31
13.2 Line Integrals
Exercise 3
Exercise 5
Exercise 9
Exercise 15
Exercise 19
Exercise 27
Exercise 33
Exercise 37
13.3 The Fundamental Theorem for Line Integrals
Exercise 9
Exercise 13
Exercise 21
Exercise 25
Exercise 27
Exercise 31
13.4 Green's Theorem
Exercise 3
Exercise 9
Exercise 11
Exercise 17
Exercise 21
Exercise 27
13.5 Curl and Divergence
Exercise 1
Exercise 9
Exercise 13
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 37
Exercise 43
Exercise 51
Exercise 53
13.7 Surface Integrals
Exercise 4
Exercise 7
Exercise 15
Exercise 19
Exercise 25
Exercise 33
Exercise 41
13.8 Stokes' Theorem
Exercise 3
Exercise 5
Exercise 15
13.9 The Divergence Theorem
Exercise 1
Exercise 7
Exercise 9
Exercise 19
Exercise 25