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

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