1 Functions and Models V1.4 Family of Functions 2 Limits V2.1 Secant Line and Tangent V2.4/4.4 Precise Definitions of Limits 3 Derivatives V3.1 Tangent Zoom V3.2 Slope-a-Scope M3.2 How do Coefficients Affect Graphs? V3.4 Slope-a-Scope (Trigonometric) M3.7 The Dynamics of Linear Motion 4 Applications of Differentiation M4.3 Using Derivatives to Sketch f V2.4/4.4 Precise Definitions of Limits V4.6 Family of Rational Functions M4.7 Analyzing Optimization Problems M4.8 Newton's Method 5 Integrals V5.1 Area Under a Parabola M5.2/8.7 Estimating Areas under Curves V5.2 Integral with Riemann Sums M5.3 Fundamental Theorem of Calculus 6 Applications of Integration V6.2A Approximating the Volume V6.2B Volumes of Revolution V6.2C A Solid With Triangular Slices 7 Inverse Functions V7.2/7.3* Slope-a-Scope (Exponential) 8 Techniques of Integration M5.2/8.7 Estimating Areas under Curves M8.8 Improper Integrals 9 Further Applications of Integration V9.1 Circumference as Limit of Polygons 10 Differential Equations M10.2A Direction Fields and Solution Curves M10.2B Euler's Method M10.4 Predator Prey 11 Parametric Equations and Polar Coordinates M11.1A Parametric Curves M11.1B Families of Cycloids M11.3 Polar Curves 12 Infinite Sequences and Series M12.2 An Unusual Series and Its Sums M12.10/12.11 Taylor and MacLaurin Series 13 Vectors and the Geometry of Space V13.2 Adding Vectors V13.3A The Dot Product of Two Vectors V13.3B Vector Projections V13.4 The Cross Product M13.6A Traces of a Surface M13.6B Quadric Surfaces 14 Vector Functions V14.1A Vector Functions and Space Curves V14.1B The Twisted Cubic Curve V13.1C Visualizing Space Curves V13.2 Secant and Tangent Vectors V14.3A The Unit Tangent Vector V14.3B The TNB Frame V14.3C Osculating Circle V14.4 Velocity and Acceleration Vectors 15 Partial Derivatives V15.1A Animated Level Curves V15.1B Level Curves of a Surface V15.2 Limit that Does Not Exist V15.4 The Tangent Plane of a Surface V15.6A Directional Derivatives V15.6B Maximizing Directional Derivative M15.7 Critical Points from Contour Maps V15.7 Families of Surfaces V15.8 Lagrange Multipliers 16 Multiple Integrals V16.2 Fubini's Theorem V16.6 Regions of Triple Integrals M16.8 Surfaces in Cyl. and Sph. Coords V16.8 Region in Spherical Coordinates 17 Vector Calculus V17.1 Vector Fields V17.6 Grid Curves on Parametric Surface M17.6 Families of Parametric Surfaces V17.7 A Nonorientable Surface

1 Functions and Models 1.1 Four Ways to Represent a Function Exercise 2 Exercise 9 Exercise 11 Exercise 13 Exercise 39 Exercise 43 Exercise 47 Exercise 55 Exercise 59 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 29 Exercise 35 Exercise 46 Exercise 53 Exercise 65 1.4 Graphing Calculators and Computers Exercise 8 Exercise 23 Exercise 27 Exercise 29 Exercise 33 2 Limits 2.1 The Tangent and Velocity Problems Exercise 3 Exercise 5 Exercise 9 2.2 The Limit of a Function Exercise 4 Exercise 11 Exercise 15 Exercise 27 Exercise 35 Exercise 42 2.3 Calculating Limits Using the Limit Laws Exercise 8 Exercise 15 Exercise 19 Exercise 20 Exercise 35 Exercise 39 Exercise 49 Exercise 58 Exercise 61 2.4 The Precise Definition of a Limit Exercise 3 Exercise 17 Exercise 25 Exercise 29 Exercise 31 Exercise 37 Exercise 43 2.5 Continuity Exercise 3 Exercise 7 Exercise 11 Exercise 18 Exercise 27 Exercise 32 Exercise 39 Exercise 41 Exercise 47 Exercise 61 3 Derivatives 3.1 Derivatives and Rates of Change Exercise 5 Exercise 7 Exercise 9 Exercise 13 Exercise 17 Exercise 18 Exercise 19 Exercise 23 Exercise 27 Exercise 35 Exercise 39 Exercise 43 Exercise 45 Exercise 47 Exercise 51 3.2 The Derivative as a Function Exercise 3b Exercise 3c Exercise 5 Exercise 11 Exercise 15a Exercise 15b Exercise 23 Exercise 25 Exercise 31 Exercise 33 Exercise 39 Exercise 45 Exercise 49 Exercise 51 3.3 Differentiation Formulas Exercise 25 Exercise 41 Exercise 52 Exercise 53 Exercise 58 Exercise 61 Exercise 63 Exercise 70 Exercise 71 Exercise 79 Exercise 81 Exercise 93 Exercise 99 3.4 Derivatives of Trigonometric Functions Exercise 9 Exercise 29 Exercise 33 Exercise 37 Exercise 41 Exercise 45 Exercise 51 3.5 The Chain Rule Exercise 5 Exercise 19 Exercise 37 Exercise 59 Exercise 61 Exercise 65 Exercise 67 Exercise 73 Exercise 75 Exercise 80 Exercise 87 3.6 Implicit Differentiation Exercise 15 Exercise 27 Exercise 39 Exercise 47 Exercise 49 3.7 Rates of Change in the Natural and Social Sciences Exercise 1g Exercise 1h Exercise 1i Exercise 15 Exercise 19 Exercise 21 Exercise 26 Exercise 29 Exercise 33 3.8 Related Rates Exercise 12 Exercise 15 Exercise 19 Exercise 25 Exercise 27 Exercise 31 Exercise 37a Exercise 37b Exercise 43 3.9 Linear Approximations and Differentials Exercise 3 Exercise 5 Exercise 9 Exercise 13 Exercise 29 Exercise 31 Exercise 38 Exercise 41 4 Applications of Differentiation 4.1 Maximum and Minimum Values Exercise 9 Exercise 11 Exercise 13 Exercise 25 Exercise 39 Exercise 41 Exercise 47 Exercise 61 Exercise 72 4.2 The Mean Value Theorem Exercise 5 Exercise 11 Exercise 19 Exercise 23 Exercise 25 Exercise 33 4.3 How Derivatives Affect the Shape of a Graph Exercise 5 Exercise 7 Exercise 11a Exercise 11b Exercise 11c Exercise 21 Exercise 27 Exercise 35 Exercise 37a Exercise 37b Exercise 37c Exercise 43 Exercise 51 Exercise 52 Exercise 53 Exercise 59 4.4 Limits at Infinity; Horizontal Asymptotes Exercise 2 Exercise 13 Exercise 19 Exercise 35 Exercise 51 Exercise 57 Exercise 59 Exercise 65a Exercise 65b 4.5 Summary of Curve Sketching Exercise 5 Exercise 9 Exercise 17 Exercise 19 Exercise 33 Exercise 43 4.6 Graphing with Calculus and Calculators Exercise 11 Exercise 23 4.7 Optimization Problems Exercise 13 Exercise 16 Exercise 17 Exercise 19 Exercise 22 Exercise 30 Exercise 33 Exercise 49 Exercise 50 Exercise 53 Exercise 55 Exercise 63 4.8 Newton's Method Exercise 4 Exercise 24 Exercise 29 Exercise 39 4.9 Antiderivatives Exercise 13 Exercise 21 Exercise 35 Exercise 43 Exercise 47 Exercise 51 Exercise 59 Exercise 67 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 33 Exercise 37 Exercise 47 Exercise 49 Exercise 53 5.3 The Fundamental Theorem of Calculus Exercise 3 Exercise 9 Exercise 13 Exercise 17 Exercise 45 Exercise 47 Exercise 54 Exercise 55 Exercise 64 Exercise 65 5.4 Indefinite Integrals and the Net Change Theorem Exercise 2 Exercise 9 Exercise 29 Exercise 41 Exercise 46 Exercise 49 Exercise 55 Exercise 57 Exercise 72 5.5 The Substitution Rule Exercise 3 Exercise 17 Exercise 23 Exercise 46 Exercise 57 Exercise 61 Exercise 65 Exercise 67 Exercise 69 Exercise 73 Exercise 79 6 Applications of Integration 6.1 Areas Between Curves Exercise 13 Exercise 21 Exercise 29 Exercise 45 Exercise 51 Exercise 53 Exercise 56 6.2 Volumes Exercise 7 Exercise 9 Exercise 11 Exercise 43 Exercise 49 Exercise 51 Exercise 57 Exercise 63 Exercise 67 6.3 Volumes by Cylindrical Shells Exercise 13 Exercise 17 Exercise 25 Exercise 29 Exercise 41 Exercise 45 6.4 Work Exercise 7 Exercise 9 Exercise 13 Exercise 17 Exercise 19 Exercise 27 6.5 Average Value of a Function Exercise 7 Exercise 9 Exercise 13 Exercise 17 Exercise 23 7 Inverse Functions 7.1 Inverse Functions Exercise 3 Exercise 8 Exercise 15 Exercise 21 Exercise 24 Exercise 39 Exercise 41 7.2 Exponential Functions and Their Derivatives Exercise 5 Exercise 9 Exercise 11 Exercise 13 Exercise 17 Exercise 21 Exercise 33 Exercise 37 Exercise 48 Exercise 49 Exercise 55 Exercise 67 Exercise 75 Exercise 81 Exercise 86 7.2star The Natural Logarithmic Function Exercise 23 Exercise 28 Exercise 37 Exercise 45 Exercise 69 Exercise 87 7.3 Logarithmic Function Exercise 23 Exercise 27a Exercise 27b Exercise 34 Exercise 39 Exercise 47 Exercise 57 7.3star The Natural Exponential Function Exercise 7 Exercise 12 Exercise 25 Exercise 35 Exercise 39 Exercise 50 Exercise 51 Exercise 57 Exercise 69 Exercise 77 Exercise 83 Exercise 88 7.4 Derivatives of Logarithmic Function Exercise 16 Exercise 21 Exercise 31 Exercise 45 Exercise 47 Exercise 54 Exercise 59 Exercise 75 Exercise 91 7.4star General Logarithmic and Exponential Function Exercise 12 Exercise 17 Exercise 19 Exercise 29 Exercise 37 Exercise 45 Exercise 49 Exercise 54 7.5 Exponential Growth and Decay Exercise 5 Exercise 9 Exercise 13 Exercise 19 7.6 Inverse Trigonometric Functions Exercise 13 Exercise 25 Exercise 31 Exercise 37 Exercise 45 7.7 Hyperbolic Functions Exercise 9 Exercise 15 Exercise 17 Exercise 35 Exercise 45 Exercise 51 Exercise 53a Exercise 53b 7.8 Indeterminate Forms and L'Hospital's Rule Exercise 1 Exercise 21 Exercise 29 Exercise 43 Exercise 48 Exercise 55 Exercise 69 Exercise 77 Exercise 91 Exercise 93 8 Techniques of Integration 8.1 Integration by Parts Exercise 3 Exercise 15 Exercise 17 Exercise 20 Exercise 35 Exercise 47 Exercise 57 Exercise 63 Exercise 66 8.2 Trigonometric Integrals Exercise 3 Exercise 7 Exercise 13 Exercise 23 Exercise 29 Exercise 43 Exercise 55 Exercise 61 8.3 Trigonometric Substitution Exercise 3 Exercise 7 Exercise 13 Exercise 17 Exercise 22 Exercise 31a Exercise 31b 8.4 Integration of Rational Functions by Partial Fractions Exercise 5 Exercise 11 Exercise 17 Exercise 25 Exercise 29 Exercise 31 Exercise 43 Exercise 47 Exercise 55 8.5 Strategy for Integration Exercise 7 Exercise 17 Exercise 23 Exercise 31 Exercise 41 Exercise 45 Exercise 49 Exercise 57 Exercise 61 Exercise 69 8.6 Integration Using Tables and Computer Algebra Systems Exercise 10 Exercise 17 Exercise 19 Exercise 26 Exercise 27 Exercise 29 Exercise 33 8.7 Approximate Integration Exercise 1 Exercise 3 Exercise 4 Exercise 33 Exercise 35 Exercise 45 8.8 Improper Integrals Exercise 1 Exercise 7 Exercise 13 Exercise 21 Exercise 29 Exercise 31 Exercise 43 Exercise 49 Exercise 57 Exercise 61 Exercise 69 9 Further Applications of Integration 9.1 Arc Length Exercise 7 Exercise 11 Exercise 13 Exercise 31 Exercise 33 Exercise 39 Exercise 42 9.2 Area of a Surface of Revolution Exercise 1a Exercise 1b Exercise 5 Exercise 11 Exercise 15 Exercise 25 Exercise 31 9.3 Applications to Physics and Engineering Exercise 7 Exercise 13 Exercise 27 Exercise 31 Exercise 41 9.4 Applications to Economics and Biology Exercise 3 Exercise 5 Exercise 10 Exercise 17 9.5 Probability Exercise 1 Exercise 7 Exercise 8 Exercise 13 10 Differential Equations 10.1 Modeling with Differential Equations Exercise 3 Exercise 7 Exercise 9 Exercise 11 Exercise 13 10.2 Direction Fields and Eulerís Method Exercise 3 Exercise 11 Exercise 13 Exercise 18 Exercise 19 Exercise 21 Exercise 23 10.3 Separable Equations Exercise 10 Exercise 15 Exercise 25 Exercise 31 Exercise 35 Exercise 39 Exercise 45 10.4 Models for Population Growth Exercise 1 Exercise 3 Exercise 7 Exercise 9 Exercise 14 Exercise 15 Exercise 17 10.5 Linear Equations Exercise 5 Exercise 9 Exercise 19 Exercise 25 Exercise 31 Exercise 33 10.6 Predator-Prey Systems Exercise 1 Exercise 3 Exercise 5 Exercise 7 11 Parametric Equations and Polar Coordinates 11.1 Curves Defined by Parametric Equations Exercise 4 Exercise 9 Exercise 13 Exercise 21 Exercise 31 Exercise 33 Exercise 34 Exercise 41 Exercise 47 Exercise 49 11.2 Calculus with Parametric Curves Exercise 5 Exercise 11 Exercise 23 Exercise 25 Exercise 31 Exercise 41 Exercise 45 Exercise 61 Exercise 65 11.3 Polar Coordinates Exercise 11 Exercise 17 Exercise 25 Exercise 35 Exercise 39 Exercise 49 Exercise 55 Exercise 59 Exercise 63 Exercise 69 11.4 Areas and Lengths in Polar Coordinates Exercise 7 Exercise 11 Exercise 21 Exercise 27 Exercise 31 Exercise 41 Exercise 47 11.5 Conic Sections Exercise 5 Exercise 15 Exercise 19 Exercise 27 Exercise 33 Exercise 37 Exercise 47 11.6 Conic Sections in Polar Coordinates Exercise 3 Exercise 13a Exercise 13b Exercise 13c Exercise 13d Exercise 21 Exercise 27 12 Infinite Sequences and Series 12.1 Sequences Exercise 13 Exercise 19 Exercise 35 Exercise 36 Exercise 43 Exercise 54 Exercise 59 Exercise 61 Exercise 69 12.2 Series Exercise 3 Exercise 9 Exercise 17 Exercise 31 Exercise 35 Exercise 41 Exercise 47 Exercise 55 Exercise 59 Exercise 65 Exercise 71 Exercise 73 12.3 The Integral Test and Estimates of Sums Exercise 7 Exercise 11 Exercise 17 Exercise 21 Exercise 33 Exercise 39 12.4 The Comparison Tests Exercise 1 Exercise 8 Exercise 10 Exercise 17 Exercise 31 Exercise 37 Exercise 41 12.5 Alternating Series Exercise 3 Exercise 7 Exercise 11 Exercise 13 Exercise 17 Exercise 23 Exercise 32 12.6 Absolute Convergence and the Ratio and Root Tests Exercise 4 Exercise 13 Exercise 19 Exercise 21 Exercise 29 Exercise 31 Exercise 33 12.8 Power Series Exercise 3 Exercise 7 Exercise 15 Exercise 23 Exercise 24 Exercise 29 Exercise 37 12.9 Representations of Functions as Power Series Exercise 5 Exercise 8 Exercise 13a Exercise 13b Exercise 15 Exercise 21 Exercise 23 Exercise 35 Exercise 37 12.10 Taylor and Maclaurin Series Exercise 5 Exercise 15 Exercise 27 Exercise 33 Exercise 35 Exercise 39 Exercise 45 Exercise 57 Exercise 59 Exercise 63 12.11 Applications of Taylor Polynomials Exercise 5 Exercise 9 Exercise 18 Exercise 19 Exercise 25 Exercise 31 Exercise 33 13 Vectors and the Geometry of Space 13.1 Three-Dimensional Coordinate Systems Exercise 5 Exercise 13 Exercise 21 Exercise 27 Exercise 31 Exercise 35 Exercise 39 13.2 Vectors Exercise 3 Exercise 11 Exercise 23 Exercise 25 Exercise 39 Exercise 41 Exercise 45 13.3 The Dot Product Exercise 19 Exercise 27 Exercise 41 Exercise 43 Exercise 49 Exercise 51 Exercise 57 13.4 The Cross Product Exercise 7 Exercise 13 Exercise 16 Exercise 19 Exercise 29 Exercise 31 Exercise 43 Exercise 45 Exercise 49 13.5 Equations of Lines and Planes Exercise 5 Exercise 9 Exercise 13 Exercise 19 Exercise 31 Exercise 49 Exercise 61 Exercise 73 13.6 Cylinders and Quadric Surfaces Exercise 9 Exercise 19 14 Vector Functions 14.1 Vector Functions and Space Curves Exercise 13 Exercise 19 Exercise 25 Exercise 39 14.2 Derivatives and Integrals of Vector Functions Exercise 1 Exercise 3 Exercise 15 Exercise 19 Exercise 25 Exercise 49 14.3 Arc Length and Curvature Exercise 3 Exercise 5 Exercise 17 Exercise 31 Exercise 33 Exercise 43 Exercise 49 Exercise 51 14.4 Motion in Space: Velocity and Acceleration Exercise 11 Exercise 19 Exercise 22 Exercise 25 Exercise 35 15 Partial Derivatives 15.1 Functions of Several Variables Exercise 1 Exercise 5 Exercise 13 Exercise 17 Exercise 23 Exercise 33 Exercise 43 Exercise 55 Exercise 61 Exercise 65 15.2 Limits and Continuity Exercise 9 Exercise 13 Exercise 21 Exercise 25 Exercise 28 Exercise 37 Exercise 39 15.3 Partial Derivatives Exercise 1 Exercise 5a Exercise 5b Exercise 21 Exercise 31 Exercise 50 Exercise 69 Exercise 81 Exercise 86 Exercise 87 15.4 Tangent Planes and Linear Approximations Exercise 11 Exercise 21 Exercise 31 Exercise 35 Exercise 37 Exercise 43 Exercise 45 15.5 The Chain Rule Exercise 11 Exercise 17 Exercise 32 Exercise 35 Exercise 39 Exercise 45 Exercise 47 15.6 Directional Derivatives and the Gradient Vector Exercise 11 Exercise 19 Exercise 23 Exercise 27 Exercise 29 Exercise 33 Exercise 43 Exercise 57 Exercise 63 15.7 Maximum and Minimum Values Exercise 1 Exercise 3 Exercise 13 Exercise 31 Exercise 41 Exercise 43 Exercise 51 15.8 Lagrange Multipliers Exercise 1 Exercise 3 Exercise 11 Exercise 19 Exercise 25 Exercise 35 Exercise 45 16 Multiple Integrals 16.1 Double Integrals over Rectangles Exercise 1 Exercise 7 Exercise 9a Exercise 9b Exercise 13 Exercise 17 16.2 Iterated Integrals Exercise 3 Exercise 9 Exercise 17 Exercise 19 Exercise 23 Exercise 27 Exercise 35 16.3 Double Integrals over General Regions Exercise 5 Exercise 13 Exercise 17 Exercise 21 Exercise 43 Exercise 45 Exercise 51 Exercise 58 16.4 Double Integrals in Polar Coordinates Exercise 1 Exercise 11 Exercise 13 Exercise 15 Exercise 25 Exercise 35 16.5 Applications of Double Integrals Exercise 1 Exercise 5 Exercise 15 Exercise 27 Exercise 29 16.6 Triple Integrals Exercise 11 Exercise 19 Exercise 23 Exercise 27 Exercise 35 Exercise 39 16.7 Triple Integrals in Cylindrical Coordinates Exercise 3 Exercise 9 Exercise 17 Exercise 21 16.8 Triple Integrals in Spherical Coordinates Exercise 1 Exercise 5 Exercise 17 Exercise 21 Exercise 30 Exercise 35 16.9 Change of Variables in Multiple Integrals Exercise 7 Exercise 13 Exercise 21 17 Vector Calculus 17.1 Vector Fields Exercise 5 Exercise 11 Exercise 17 Exercise 23 Exercise 29 Exercise 35 17.2 Line Integrals Exercise 3 Exercise 7 Exercise 11 Exercise 17 Exercise 21 Exercise 33 Exercise 39 Exercise 43 17.3 The Fundamental Theorem for Line Integrals Exercise 7 Exercise 11 Exercise 15 Exercise 23 Exercise 27 Exercise 29 Exercise 33 17.4 Green's Theorem Exercise 3 Exercise 7 Exercise 9 Exercise 17 Exercise 21 Exercise 27 17.5 Curl and Divergence Exercise 1 Exercise 11 Exercise 15 Exercise 19 Exercise 21 Exercise 31 17.6 Parametric Surfaces and Their Areas Exercise 3 Exercise 13 Exercise 19 Exercise 23 Exercise 26 Exercise 33 Exercise 37 Exercise 41 Exercise 47 Exercise 55 Exercise 57 17.7 Surface Integrals Exercise 4 Exercise 5 Exercise 15 Exercise 19 Exercise 25 Exercise 37 Exercise 45 17.8 Stokes' Theorem Exercise 5 Exercise 7 Exercise 15 Exercise 19 17.9 The Divergence Theorem Exercise 1 Exercise 7 Exercise 9 Exercise 19 Exercise 25 18 Second-Order Differential Equations 18.1 Second-Order Linear Equations Exercise 1 Exercise 9 Exercise 11 Exercise 17 Exercise 21 Exercise 23 Exercise 30 18.2 Nonhomogeneous Linear Equations Exercise 5 Exercise 9 Exercise 16 Exercise 18 Exercise 21a Exercise 21b Exercise 25 18.3 Applications of Second-Order Differential Equations Exercise 3 Exercise 9 Exercise 13 Exercise 17 18.4 Series Solutions Exercise 3 Exercise 9