1 Functions and Models V1.4 Family of Functions M1.5 Exponential Functions 2 Limits and Derivatives V2.1 Secant Line and Tangent M2.4/2.6 PreciseDefinitionsOfLimits V2.7 Tangent Zoom V2.8 Slope-a-Scope M2.8 How do Coefficients Affect Graphs? 3 Differentiation Rules V3.1 Slope-a-Scope (Exponential) V3.3 Slope-a-Scope (Trigonometric) M3.7 The Dynamics of Linear Motion 4 Applications of Differentiation M4.3 Using Derivatives to Sketch f V4.6 Family of Rational Functions M4.7 Analyzing Optimization Problems M4.8 Newton's Method 5 Integrals V5.1 Area Under a Parabola M5.2/7.7 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 Techniques of Integrations M5.2/7.7 Estimating Areas under Curves M7.8 Improper Integrals 8 Further Applications of Integration V8.1 Circumference as Limit of Polygons 9 Differential Equations M9.2A Direction Fields and Solution Curves M9.2B Euler's Method M9.4 Predator Prey 10 Parametric Equations and Polar Coordinates M10.1A Parametric Curves M10.1B Families of Cycloids M10.3 Polar Curves 11 Infinite Sequences and Series M11.2 An Unusual Series and Its Sums M11.10/11.11 Taylor and MacLaurin Series 12 Vectors and the Geometry of Space V12.2 Adding Vectors V12.3A The Dot Product of Two Vectors V12.3B Vector Projections V12.4 The Cross Product M12.6A Traces of a Surface M12.6B Quadric Surfaces 13 Vector Functions V13.1A Vector Functions and Space Curves V13.1B The Twisted Cubic Curve V13.1C Visualizing Space Curves V13.2 Secant and Tangent Vectors V13.3A The Unit Tangent Vector V13.3B The TNB Frame V13.3C Osculating Circle V13.4 Velocity and Acceleration Vectors 14 Partial Derivatives V14.1A Animated Level Curves V14.1B Level Curves of a Surface V14.2 Limit that Does Not Exist V14.4 The Tangent Plane of a Surface V14.6A Directional Derivatives V14.6B Maximizing Directional Derivative M14.7 Critical Points from Contour Maps V14.7 Families of Surfaces V14.8 Lagrange Multipliers 15 Multiple Integrals V15.2 Fubini's Theorem V15.6 Regions of Triple Integrals M15.8 Surfaces in Cyl. and Sph. Coords V15.8 Region in Spherical Coordinates 16 Vector Calculus V16.1 Vector Fields V16.6 Grid Curves on Parametric Surface M16.6 Families of Parametric Surfaces V16.7 A Nonorientable Surface

1 Functions and Models 1.1 Four Ways to Represent a Function Exercise 2 Exercise 9 Exercise 11 Exercise 13 Exercise 23 Exercise 31 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 35a Exercise 35d Exercise 46 Exercise 53 Exercise 65 1.4 Graphing Calculators and Computers Exercise 8 Exercise 9 Exercise 23 Exercise 27 Exercise 29 Exercise 33 1.5 Exponential Functions Exercise 5 Exercise 9 Exercise 11 Exercise 13 Exercise 17 Exercise 23 1.6 Inverse Functions and Logarithms Exercise 3 Exercise 8 Exercise 13 Exercise 17 Exercise 19 Exercise 22 Exercise 23 Exercise 25 Exercise 43 Exercise 45 Exercise 49a Exercise 49b Exercise 67 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 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 Exercise 3 Exercise 7 Exercise 11 Exercise 18 Exercise 27 Exercise 29 Exercise 32 Exercise 39 Exercise 41 Exercise 47 Exercise 53 Exercise 61 2.6 Limits at Infinity; Horizontal Asymptotes Exercise 2 Exercise 7 Exercise 19 Exercise 25 Exercise 41 Exercise 55 Exercise 57 Exercise 65a Exercise 65b 2.7 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 2.8 The Derivative as a Function Exercise 3b Exercise 3c Exercise 5 Exercise 11 Exercise 17a Exercise 17b Exercise 25 Exercise 27 Exercise 33 Exercise 35 Exercise 41 Exercise 47 Exercise 51 Exercise 53 3 Differentiation Rules 3.1 Derivatives of Polynomials and Exponential Functions Exercise 23 Exercise 31 Exercise 35 Exercise 46 Exercise 49 Exercise 51 Exercise 59 Exercise 73 Exercise 77 3.2 The Product and Quotient Rules Exercise 11 Exercise 25 Exercise 33 Exercise 36 Exercise 40 Exercise 43 Exercise 45 Exercise 50 Exercise 51 Exercise 55 3.3 Derivatives of Trigonometric Functions Exercise 9 Exercise 22 Exercise 29 Exercise 33 Exercise 37 Exercise 41 Exercise 45 Exercise 51 3.4 The Chain Rule Exercise 5 Exercise 19 Exercise 23 Exercise 37 Exercise 55 Exercise 59 Exercise 61 Exercise 65 Exercise 67 Exercise 75 Exercise 77 Exercise 84 Exercise 93 3.5 Implicit Differentiation Exercise 15 Exercise 27 Exercise 39 Exercise 47 Exercise 61 Exercise 63 Exercise 67a Exercise 67b 3.6 Derivatives of Logarithmic Functions Exercise 19 Exercise 27 Exercise 41 Exercise 43 Exercise 50 Exercise 53 3.7 Rates of Change in the Natural and Social Sciences Exercise 1g Exercise 1h Exercise 1i Exercise 15 Exercise 19 Exercise 21 Exercise 28 Exercise 31 Exercise 35 3.8 Exponential Growth and Decay Exercise 3 Exercise 5 Exercise 9 Exercise 13 Exercise 19 3.9 Related Rates Exercise 12 Exercise 15 Exercise 19 Exercise 25 Exercise 27 Exercise 31 Exercise 37a Exercise 37b Exercise 43 3.10 Linear Approximations and Differentials Exercise 3 Exercise 5 Exercise 9 Exercise 13 Exercise 15 Exercise 29 Exercise 33 Exercise 40 Exercise 43 3.11 Hyperbolic Functions Exercise 9 Exercise 15 Exercise 17 Exercise 35 Exercise 45 Exercise 51 Exercise 53 4 Applications of Differentiation 4.1 Maximum and Minimum Values Exercise 9 Exercise 11 Exercise 13 Exercise 25 Exercise 39 Exercise 41 Exercise 49 Exercise 67 Exercise 78 4.2 The Mean Value Theorem Exercise 5 Exercise 11 Exercise 19 Exercise 23 Exercise 25 Exercise 35 4.3 How Derivatives Affect the Shape of a Graph Exercise 5a Exercise 5b Exercise 7 Exercise 11a Exercise 11b Exercise 11c Exercise 17 Exercise 25 Exercise 31 Exercise 39 Exercise 41a Exercise 41b Exercise 41c Exercise 51 Exercise 51d Exercise 55 Exercise 63 Exercise 64 Exercise 67 Exercise 75 4.4 Indeterminate Forms and L'Hospital's Rule Exercise 1 Exercise 21 Exercise 29 Exercise 43 Exercise 48 Exercise 55 Exercise 69 Exercise 81 4.5 Summary of Curve Sketching Exercise 5 Exercise 9 Exercise 17 Exercise 19 Exercise 33 Exercise 41 Exercise 57 4.6 Graphing with Calculus and Calculators Exercise 11 Exercise 13 Exercise 23 Exercise 30 Exercise 31 Exercise 34 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 Exercise 69 4.8 Newton's Method Exercise 4 Exercise 24 Exercise 31 Exercise 37 Exercise 41 4.9 Antiderivatives Exercise 13 Exercise 21 Exercise 23 Exercise 39 Exercise 49 Exercise 53 Exercise 57 Exercise 65 Exercise 73 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 51 Exercise 53 Exercise 62 Exercise 63 Exercise 72 Exercise 73 Exercise 74 5.4 Indefinite Integrals and the Net Change Theorem Exercise 2 Exercise 9 Exercise 23 Exercise 31 Exercise 43 Exercise 48 Exercise 51 Exercise 57 Exercise 59 5.5 The Substitution Rule Exercise 3 Exercise 13 Exercise 19 Exercise 21 Exercise 25 Exercise 33 Exercise 43 Exercise 59 Exercise 64 Exercise 67 Exercise 75 Exercise 81 Exercise 85 6 Applications of Integration 6.1 Areas between Curves Exercise 3 Exercise 9 Exercise 13 Exercise 21 Exercise 29 Exercise 45 Exercise 51 Exercise 53 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 5 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 Techniques of Integrations 7.1 Integration by Parts Exercise 3 Exercise 15 Exercise 17 Exercise 20 Exercise 35 Exercise 47 Exercise 57 Exercise 63 Exercise 66 7.2 Trigonometric Integrals Exercise 3 Exercise 7 Exercise 13 Exercise 23 Exercise 29 Exercise 43 Exercise 55 Exercise 61 7.3 Trigonometric Substitution Exercise 3 Exercise 7 Exercise 13 Exercise 17 Exercise 22 Exercise 31a Exercise 31b 7.4 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 7.5 Strategy for Integration Exercise 7 Exercise 17 Exercise 23 Exercise 31 Exercise 41 Exercise 45 Exercise 49 Exercise 57 Exercise 61 Exercise 69 7.6 Integration Using Tables and Computer Algebra Systems Exercise 10 Exercise 17 Exercise 19 Exercise 26 Exercise 27 Exercise 29 Exercise 33 7.7 Approximate Integration Exercise 1 Exercise 3 Exercise 4 Exercise 33 Exercise 35 Exercise 45 7.8 Improper Integrals Exercise 1 Exercise 7 Exercise 13 Exercise 21 Exercise 29 Exercise 31 Exercise 43 Exercise 49 Exercise 57 Exercise 61 Exercise 69 8 Further Applications of Integration 8.1 Arc Length Exercise 7 Exercise 11 Exercise 13 Exercise 31 Exercise 33 Exercise 39 Exercise 42 8.2 Area of a Surface of Revolution Exercise 1a Exercise 1b Exercise 5 Exercise 11 Exercise 15 Exercise 25 Exercise 31 8.3 Applications to Physics and Engineering Exercise 7 Exercise 13 Exercise 27 Exercise 31 Exercise 41 8.4 Applications to Economics and Biology Exercise 3 Exercise 5 Exercise 10 Exercise 17 8.5 Probability Exercise 1 Exercise 7 Exercise 8 Exercise 13 9 Differential Equations 9.1 Modeling with Differential Equations Exercise 3 Exercise 7 Exercise 9 Exercise 11 Exercise 13 9.2 Direction Fields and Eulerís Method Exercise 3 Exercise 11 Exercise 13 Exercise 18 Exercise 19 Exercise 21 Exercise 23 9.3 Separable Equations Exercise 10 Exercise 15 Exercise 25 Exercise 31 Exercise 35 Exercise 39 Exercise 45 9.4 Models for Population Growth Exercise 1 Exercise 3 Exercise 7 Exercise 9 Exercise 14 Exercise 15 Exercise 17 9.5 Linear Equations Exercise 5 Exercise 9 Exercise 19 Exercise 25 Exercise 31 Exercise 33 9.6 Predator-Prey Systems Exercise 1 Exercise 3 Exercise 5 Exercise 7 10 Parametric Equations and Polar Coordinates 10.1 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 10.2 Calculus with Parametric Curves Exercise 5 Exercise 11 Exercise 23 Exercise 25 Exercise 31 Exercise 41 Exercise 45 Exercise 61 Exercise 65 10.3 Polar Coordinates Exercise 11 Exercise 17 Exercise 25 Exercise 35 Exercise 39 Exercise 49 Exercise 55 Exercise 59 Exercise 63 Exercise 69 10.4 Areas and Lengths in Polar Coordinates Exercise 7 Exercise 11 Exercise 21 Exercise 27 Exercise 31 Exercise 41 Exercise 47 10.5 Conic Sections Exercise 5 Exercise 15 Exercise 19 Exercise 27 Exercise 33 Exercise 37 Exercise 47 10.6 Conic Sections in Polar Coordinates Exercise 3 Exercise 13 Exercise 13b Exercise 13c Exercise 13d Exercise 21 Exercise 27 11 Infinite Sequences and Series 11.1 Sequences Exercise 13 Exercise 19 Exercise 35 Exercise 36 Exercise 43 Exercise 54 Exercise 59 Exercise 61 Exercise 69 11.2 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 11.3 The Integral Test and Estimates of Sums Exercise 7 Exercise 11 Exercise 17 Exercise 21 Exercise 33 Exercise 39 11.4 The Comparison Tests Exercise 1 Exercise 8 Exercise 10 Exercise 17 Exercise 31 Exercise 37 Exercise 41 11.5 Alternating Series Exercise 3 Exercise 7 Exercise 11 Exercise 13 Exercise 17 Exercise 23 Exercise 32 11.6 Absolute Convergence and the Ratio and Root Tests Exercise 4 Exercise 13 Exercise 19 Exercise 21 Exercise 29 Exercise 31 Exercise 33 11.8 Power Series Exercise 3 Exercise 7 Exercise 15 Exercise 23 Exercise 24 Exercise 29 Exercise 37 11.9 Representations of Functions as Power Series Exercise 5 Exercise 8 Exercise 13a Exercise 13b Exercise 15 Exercise 21 Exercise 23 Exercise 35 Exercise 37 11.10 Taylor and Maclaurin Series Exercise 5 Exercise 15 Exercise 27 Exercise 33 Exercise 35 Exercise 39 Exercise 45 Exercise 57 Exercise 59 Exercise 63 11.11 Applications of Taylor Polynomials Exercise 5 Exercise 9 Exercise 18 Exercise 19 Exercise 25 Exercise 31 Exercise 33 12 Vectors and the Geometry of Space 12.1 Three-Dimensional Coordinate Systems Exercise 5 Exercise 13 Exercise 21 Exercise 27 Exercise 31 Exercise 35 Exercise 39 12.2 Vectors Exercise 3 Exercise 11 Exercise 23 Exercise 25 Exercise 39 Exercise 41 Exercise 45 12.3 The Dot Product Exercise 19 Exercise 27 Exercise 41 Exercise 43 Exercise 49 Exercise 51 Exercise 57 12.4 The Cross Product Exercise 7 Exercise 13 Exercise 16 Exercise 19 Exercise 29 Exercise 31 Exercise 43 Exercise 45 Exercise 49 12.5 Equations of Lines and Planes Exercise 5 Exercise 9 Exercise 13 Exercise 19 Exercise 31 Exercise 49 Exercise 61 Exercise 73 12.6 Cylinders and Quadric Surfaces Exercise 9 Exercise 19 13 Vector Functions 13.1 Vector Functions and Space Curves Exercise 13 Exercise 19 Exercise 25 Exercise 39 13.2 Derivatives and Integrals of Vector Functions Exercise 1 Exercise 3 Exercise 15 Exercise 19 Exercise 25 Exercise 49 13.3 Arc Length and Curvature Exercise 3 Exercise 5 Exercise 17 Exercise 31 Exercise 33 Exercise 43 Exercise 49 Exercise 51 13.4 Motion in Space: Velocity and Acceleration Exercise 11 Exercise 19 Exercise 22 Exercise 25 Exercise 35 14 Partial Derivatives 14.1 Functions of Several Variables Exercise 1 Exercise 5 Exercise 13 Exercise 17 Exercise 23 Exercise 33 Exercise 43 Exercise 55 Exercise 61 Exercise 65 14.2 Limits and Continuity Exercise 9 Exercise 13 Exercise 21 Exercise 25 Exercise 28 Exercise 37 Exercise 39 14.3 Partial Derivatives Exercise 1 Exercise 5a Exercise 5b Exercise 21 Exercise 31 Exercise 50 Exercise 69 Exercise 81 Exercise 86 Exercise 87 14.4 Tangent Planes and Linear Approximations Exercise 11 Exercise 21 Exercise 31 Exercise 35 Exercise 37 Exercise 43 Exercise 45 14.5 The Chain Rule Exercise 11 Exercise 17 Exercise 32 Exercise 35 Exercise 39 Exercise 45 Exercise 47 14.6 Directional Derivatives and the Gradient Vector Exercise 11 Exercise 19 Exercise 23 Exercise 27 Exercise 29 Exercise 33 Exercise 43 Exercise 57 Exercise 63 14.7 Maximum and Minimum Values Exercise 1 Exercise 3 Exercise 13 Exercise 31 Exercise 41 Exercise 43 Exercise 51 14.8 Lagrange Multipliers Exercise 1 Exercise 3 Exercise 11 Exercise 19 Exercise 25 Exercise 35 Exercise 45 15 Multiple Integrals 15.1 Double Integrals over Rectangles Exercise 1 Exercise 7 Exercise 9a Exercise 9b Exercise 13 Exercise 17 15.2 Iterated Integrals Exercise 3 Exercise 9 Exercise 17 Exercise 19 Exercise 23 Exercise 27 Exercise 35 15.3 Double Integrals over General Regions Exercise 5 Exercise 13 Exercise 17 Exercise 21 Exercise 43 Exercise 45 Exercise 51 Exercise 58 15.4 Double Integrals in Polar Coordinates Exercise 1 Exercise 11 Exercise 13 Exercise 15 Exercise 25 Exercise 35 15.5 Applications of Double Integrals Exercise 1 Exercise 5 Exercise 15 Exercise 27 Exercise 29 15.6 Triple Integrals Exercise 11 Exercise 19 Exercise 23 Exercise 27 Exercise 35 Exercise 39 15.7 Triple Integrals in Cylindrical Coordinates Exercise 3 Exercise 9 Exercise 17 Exercise 21 15.8 Triple Integrals in Spherical Coordinates Exercise 1 Exercise 5 Exercise 17 Exercise 21 Exercise 30 Exercise 35 15.9 Change of Variables in Multiple Integrals Exercise 7 Exercise 13 Exercise 21 16 Vector Calculus 16.1 Vector Fields Exercise 5 Exercise 11 Exercise 17 Exercise 23 Exercise 29 Exercise 35 16.2 Line Integrals Exercise 3 Exercise 7 Exercise 11 Exercise 17 Exercise 21 Exercise 33 Exercise 39 Exercise 43 16.3 The Fundamental Theorem for Line Integrals Exercise 7 Exercise 11 Exercise 15 Exercise 23 Exercise 27 Exercise 29 Exercise 33 16.4 Green's Theorem Exercise 3 Exercise 7 Exercise 9 Exercise 17 Exercise 21 Exercise 27 16.5 Curl and Divergence Exercise 1 Exercise 11 Exercise 15 Exercise 19 Exercise 21 Exercise 31 16.6 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 16.7 Surface Integrals Exercise 4 Exercise 5 Exercise 15 Exercise 19 Exercise 25 Exercise 37 Exercise 45 16.8 Stokes' Theorem Exercise 5 Exercise 7 Exercise 15 Exercise 19 16.9 The Divergence Theorem Exercise 1 Exercise 7 Exercise 9 Exercise 19 Exercise 25 17 Second-Order Differential Equations 17.1 Second-Order Linear Equations Exercise 1 Exercise 9 Exercise 11 Exercise 17 Exercise 21 Exercise 23 Exercise 30 17.2 Nonhomogeneous Linear Equations Exercise 5 Exercise 9 Exercise 16 Exercise 18 Exercise 21a Exercise 21b Exercise 25 17.3 Applications of Second-Order Differential Equations Exercise 3 Exercise 9 Exercise 13 Exercise 17 17.4 Series Solutions Exercise 3 Exercise 9 Appendixes Appendix G Appendix G Exercise 1 Exercise 3 Exercise 5