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Preview P Area of a Circle as a Limit 1 Functions and Models V1.4 Family of Functions M1.5 Exponential Functions M1.7A Parametric Curves M1.7B Families of Cycloids 2 Limits and Derivatives V2.1 Secant Line and Tangent V2.6 Tangent Zoom V2.8 Slope-a-Scope M2.8 How do Coefficients Affect Graphs? 3 Differentiation Rules V3.1 Slope-a-Scope (Exponential) M3.3 The Dynamics of Linear Motion V3.4 Slope-a-Scope (Trigonometric) 4 Applications of Differentiation M4.3 Using Derivatives to Sketch f V4.4 Family of Rational Functions M4.6 Analyzing Optimization Problems M4.8 Newton's Method 5 Integrals V5.1 Area Under a Parabola M5.2/5.9 Estimating Areas under Curves V5.2 Integral with Riemann Sums M5.4 Fundamental Theorem of Calculus M5.10 Improper Integrals 6 Applications of Integration V6.2A Approximating the Volume V6.2B Volumes of Revolution V6.2C A Solid With Triangular Slices V6.3 Circumference as Limit of Polygons 7 Differential Equations M7.2A Direction Fields and Solution Curves M7.2B Euler's Method M7.6 Predator Prey 8 Infinite Sequences and Series M8.2 An Unusual Series and Its Sums M8.7/8.9 Taylor and MacLaurin Series 9 Vectors and the Geometry of Space V9.2 Adding Vectors V9.3A The Dot Product of Two Vectors V9.3B Vector Projections V9.4 The Cross Product M9.6A Traces of a Surface M9.6B Quadric Surfaces M9.7 Surfaces in Cyl. and Sph. Coords 10 Vector Functions V10.1A Vector Functions and Space Curves V10.1B The Twisted Cubic Curve V10.1C Visualizing Space Curves V10.2 Secant and Tangent Vectors V10.3A The Unit Tangent Vector V10.3B The TNB Frame V10.3C Osculating Circle V10.4 Velocity and Acceleration Vectors V10.5 Grid Curves on Parametric Surface M10.5 Families of Parametric Surfaces 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 V11.7 Families of Surfaces V11.8 Lagrange Multipliers 12 Multiple Integrals V12.2 Fubini's Theorem V12.7 Regions of Triple Integrals V12.8 Region in Spherical Coordinates 13 Vector Calculus V13.1 Vector Fields V13.6 A Nonorientable Surface Appendixes D Precise Definitions of Limits H Polar Curves
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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 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 31 Exercise 39a Exercise 39d Exercise 46 Exercise 53 Exercise 65 1.4 Graphing Calculators and Computers Exercise 8 Exercise 9 Exercise 21 Exercise 25 Exercise 27 Exercise 31 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 25 Exercise 43 Exercise 45 Exercise 49a Exercise 49b Exercise 59 1.7 Parametric Curves Exercise 4 Exercise 7 Exercise 11 Exercise 17 Exercise 27 Exercise 29 Exercise 30 Exercise 37 Exercise 41 Exercise 43 2 Limits and Derivatives 2.1 The Tangent and Velocity Problems Exercise 3 Exercise 5 Exercise 9 2.2 Limit of a Function Exercise 4 Exercise 7 Exercise 11 Exercise 23 Exercise 28 2.3 Calculating Limits Using the Limit Law Exercise 6 Exercise 13 Exercise 17 Exercise 27 Exercise 31 Exercise 37 Exercise 43 Exercise 45 2.4 Continuity Exercise 3 Exercise 7 Exercise 11 Exercise 16 Exercise 21 Exercise 23 Exercise 26 Exercise 31 Exercise 33 Exercise 37 Exercise 43 Exercise 47 2.5 Limits Involving Infinity Exercise 2 Exercise 7 Exercise 17 Exercise 21 Exercise 25 Exercise 35 Exercise 43 Exercise 45 2.6 Tangents, Velocities, and Other Rates of Change Exercise 3 Exercise 7 Exercise 9 Exercise 11 Exercise 17 Exercise 21 Exercise 27 2.7 Derivatives Exercise 3 Exercise 4 Exercise 5 Exercise 9 Exercise 15 Exercise 23 Exercise 27 Exercise 31 Exercise 35 2.8 The Derivative as a Function Exercise 3b Exercise 3c Exercise 5 Exercise 11 Exercise 17a Exercise 17b Exercise 23 Exercise 25 Exercise 29 Exercise 31 Exercise 37 Exercise 43 Exercise 47 2.9 What Does f' Say about f'? Exercise 3 Exercise 5 Exercise 9 Exercise 10 Exercise 11 Exercise 17 Exercise 25 3 Differentiation Rules 3.1 Derivatives of Polynomials and Exponential Functions Exercise 19 Exercise 23 Exercise 25 Exercise 27 Exercise 38 Exercise 41 Exercise 44 Exercise 45 Exercise 53 Exercise 59 Exercise 61 Exercise 65 3.2 The Product and Quotient Rules Exercise 9 Exercise 19 Exercise 21 Exercise 24 Exercise 28 Exercise 31 Exercise 33 Exercise 38 Exercise 41 Exercise 43 Exercise 45 3.3 Rates of Change in the Natural and Social Sciences Exercise 13 Exercise 17 Exercise 19 Exercise 26 Exercise 29 Exercise 33 3.4 Derivatives of Trigonometric Function Exercise 7 Exercise 18 Exercise 23 Exercise 27 Exercise 29 Exercise 33 Exercise 35 Exercise 37 Exercise 39 Exercise 41 Exercise 43 3.5 The Chain Rule Exercise 5 Exercise 19 Exercise 29 Exercise 37 Exercise 41 Exercise 45 Exercise 49 Exercise 53 Exercise 57 Exercise 59 Exercise 66 Exercise 73a Exercise 73b Exercise 79 3.6 Implicit Differentiation Exercise 11 Exercise 17 Exercise 25 Exercise 31 Exercise 41 Exercise 45 Exercise 49 Exercise 53a Exercise 53b Exercise 55 3.7 Derivatives of Logarithmic Functions Exercise 17 Exercise 21 Exercise 25 Exercise 31 Exercise 38 Exercise 41 3.8 Linear Approximations and Differentials Exercise 4 Exercise 7 Exercise 9 Exercise 13 Exercise 19 Exercise 25 Exercise 27 Exercise 31 Exercise 33 4 Applications of Differentiation 4.1 Related Rates Exercise 9 Exercise 13 Exercise 17 Exercise 25 Exercise 29 Exercise 33a Exercise 33b Exercise 37 4.2 Maximum and Minimum Values Exercise 9 Exercise 11 Exercise 13 Exercise 21 Exercise 31 Exercise 33 Exercise 39 Exercise 53 Exercise 60 4.3 Derivatives and the Shapes of Curves Exercise 5 Exercise 13 Exercise 23 Exercise 35 Exercise 39 Exercise 49 Exercise 51 Exercise 53 Exercise 55 4.4 Graphing with Calculus and Calculators Exercise 11 Exercise 21 Exercise 23 Exercise 24 Exercise 28 Exercise 29 4.5 Indeterminate Forms and l'Hospital's Rule Exercise 1 Exercise 17 Exercise 29 Exercise 32 Exercise 37 Exercise 45 Exercise 49 Exercise 51 Exercise 55 Exercise 65 4.6 Optimization Problems Exercise 9 Exercise 11 Exercise 13 Exercise 18 Exercise 19 Exercise 21 Exercise 31 Exercise 33 Exercise 37 Exercise 43 4.7 Applications to Business and Economics Exercise 1 Exercise 5 Exercise 9 Exercise 15 4.8 Newton's Method Exercise 4 Exercise 14 Exercise 23 Exercise 27 Exercise 29 Exercise 31 4.9 Antiderivatives Exercise 7 Exercise 13 Exercise 15 Exercise 25 Exercise 31 Exercise 33 Exercise 39 Exercise 43 Exercise 49 Exercise 53 5 Integrals 5.1 Areas and Distances Exercise 2 Exercise 5 Exercise 11 Exercise 15 Exercise 19 5.2 The Definite Integral Exercise 5 Exercise 9 Exercise 19 Exercise 23 Exercise 31 Exercise 35 Exercise 41 Exercise 43 5.3 Evaluating Definite Integrals Exercise 7 Exercise 13 Exercise 35 Exercise 38 Exercise 41 Exercise 46 Exercise 49 Exercise 55 Exercise 57 Exercise 68 5.4 The Fundamental Theorem of Calculus Exercise 3 Exercise 9 Exercise 11 Exercise 15 Exercise 19 Exercise 24 Exercise 26 Exercise 27 5.5 The Substitution Rule Exercise 3 Exercise 11 Exercise 13 Exercise 19 Exercise 23 Exercise 33 Exercise 45 Exercise 52 Exercise 53 Exercise 59 Exercise 63 Exercise 67 5.6 Integration by Parts Exercise 3 Exercise 13 Exercise 16 Exercise 27 Exercise 37 Exercise 41 Exercise 44 5.7 Additional Techniques of Integration Exercise 3 Exercise 6 Exercise 9 Exercise 19 Exercise 21 Exercise 31 5.8 Integration Using Tables and Computer Algebra Systems Exercise 6 Exercise 11 Exercise 13 Exercise 17 Exercise 18 Exercise 21 Exercise 23 5.9 Approximate Integration Exercise 1 Exercise 3 Exercise 4 Exercise 27 Exercise 29 Exercise 37 5.10 Improper Integrals Exercise 1 Exercise 7 Exercise 13 Exercise 17 Exercise 25 Exercise 29 Exercise 35 Exercise 43 Exercise 49 Exercise 51 Exercise 57 6 Applications of Integration 6.1 More about Areas Exercise 3 Exercise 9 Exercise 11 Exercise 22 Exercise 27 Exercise 31 Exercise 37 Exercise 43 6.2 Volumes Exercise 5 Exercise 7 Exercise 9 Exercise 25 Exercise 27 Exercise 33 Exercise 39 Exercise 43 6.3 Arc Length Exercise 5 Exercise 7 Exercise 17 Exercise 19 Exercise 23 Exercise 26 6.4 Average Value of a Function Exercise 5 Exercise 9 Exercise 13 Exercise 19 6.5 Applications to Physics and Engineering Exercise 5 Exercise 9 Exercise 13 Exercise 15 Exercise 19 Exercise 25 Exercise 27 Exercise 37 Exercise 39 6.6 Applications to Economics and Biology Exercise 3 Exercise 5 Exercise 10 Exercise 15 6.7 Probability Exercise 1 Exercise 5 Exercise 6 Exercise 11 7 Differential Equations 7.1 Modeling with Differential Equations Exercise 3 Exercise 7 Exercise 9 Exercise 11 Exercise 13 7.2 Direction Fields and Euler's Method Exercise 3 Exercise 11 Exercise 13 Exercise 18 Exercise 19 Exercise 21 Exercise 23 7.3 Separable Equations Exercise 8 Exercise 9 Exercise 19 Exercise 25 Exercise 29 Exercise 33 Exercise 39 7.4 Exponential Growth and Decay Exercise 3 Exercise 5 Exercise 9 Exercise 13 Exercise 19 Exercise 22 7.5 The Logistic Equation Exercise 1 Exercise 3 Exercise 7 Exercise 9 Exercise 11 Exercise 13 7.6 Predator-Prey Systems Exercise 1 Exercise 3 Exercise 5 Exercise 7 8 Infinite Sequences and Series 8.1 Sequences Exercise 5 Exercise 9 Exercise 21 Exercise 25 Exercise 37 Exercise 41 Exercise 45 Exercise 47 8.2 Series Exercise 3 Exercise 9 Exercise 15 Exercise 25 Exercise 27 Exercise 31 Exercise 35 Exercise 41 Exercise 45 Exercise 49 Exercise 53 Exercise 55 8.3 The Integral and Comparison Tests; Estimating Sums Exercise 3 Exercise 11 Exercise 13 Exercise 15 Exercise 16 Exercise 18 Exercise 21 Exercise 25 Exercise 29 Exercise 35 Exercise 37 8.4 Other Convergence Tests Exercise 3 Exercise 7 Exercise 11 Exercise 13 Exercise 19 Exercise 24 Exercise 25 Exercise 31 Exercise 33 Exercise 35 8.5 Power Series Exercise 3 Exercise 7 Exercise 8 Exercise 13 Exercise 17 Exercise 18 Exercise 19 Exercise 25 8.6 Representations of Functions as Power Series Exercise 6 Exercise 7 Exercise 11a Exercise 11b Exercise 13 Exercise 19 Exercise 21 Exercise 33 Exercise 35 8.7 Taylor and Maclaurin Series Exercise 5 Exercise 11 Exercise 24 Exercise 29 Exercise 43 Exercise 45 Exercise 49 8.8 The Binomial Series Exercise 3 Exercise 5 Exercise 9 Exercise 13 8.9 Applications of Taylor Polynomials Exercise 3 Exercise 7 Exercise 15 Exercise 16 Exercise 21 Exercise 25 Exercise 27 9 Vectors and the Geometry of Space 9.1 Three-Dimensional Coordinate Systems Exercise 5 Exercise 11 Exercise 17 Exercise 23 Exercise 27 Exercise 31 Exercise 35 9.2 Vectors Exercise 3 Exercise 9 Exercise 19 Exercise 21 Exercise 23 Exercise 29 Exercise 33 Exercise 37 9.3 The Dot Product Exercise 9 Exercise 15 Exercise 21 Exercise 27 Exercise 29 Exercise 35 Exercise 37 Exercise 43 9.4 The Cross Product Exercise 1 Exercise 4 Exercise 9 Exercise 13 Exercise 17 Exercise 27 Exercise 29 Exercise 33 9.5 Equations of Lines and Planes Exercise 5 Exercise 7 Exercise 11 Exercise 17 Exercise 25 Exercise 39 Exercise 51 9.6 Functions and Surfaces Exercise 1 Exercise 5 Exercise 15 Exercise 25 9.7 Cylindrical and Spherical Coordinates Exercise 5 Exercise 7 Exercise 13 Exercise 17 Exercise 23 Exercise 33 10 Vector Functions 10.1 Vector Functions and Space Curves Exercise 11 Exercise 17 Exercise 19 Exercise 23 Exercise 33 Exercise 35 10.2 Derivatives and Integrals of Vector Functions Exercise 1 Exercise 3 Exercise 13 Exercise 15 Exercise 21 Exercise 25 Exercise 45 10.3 Arc Length and Curvature Exercise 3 Exercise 11 Exercise 25 Exercise 27 Exercise 31 Exercise 37 Exercise 43 Exercise 45 10.4 Motion in Space: Velocity and Acceleration Exercise 11 Exercise 17 Exercise 20 Exercise 23 Exercise 33 10.5 Parametric Surfaces Exercise 1 Exercise 13 Exercise 17 Exercise 21 Exercise 24 Exercise 29 11 Partial Derivatives 11.1 Functions of Several Variables Exercise 1 Exercise 5 Exercise 11 Exercise 19 Exercise 31 Exercise 37 Exercise 41 11.2 Limits and Continuity Exercise 7 Exercise 11 Exercise 17 Exercise 21 Exercise 24 Exercise 31 Exercise 33 11.3 Partial Derivatives Exercise 1 Exercise 5 Exercise 7 Exercise 17 Exercise 27 Exercise 46 Exercise 61 Exercise 71 Exercise 76 Exercise 77 11.4 Tangent Planes and Linear Approximations Exercise 9 Exercise 15 Exercise 23 Exercise 27 Exercise 33 Exercise 39 Exercise 41 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 1 Exercise 11 Exercise 17 Exercise 23 Exercise 25 Exercise 29 Exercise 37 Exercise 47 Exercise 53 11.7 Maximum and Minimum Values Exercise 1 Exercise 3 Exercise 11 Exercise 27 Exercise 35 Exercise 37 Exercise 45 11.8 Lagrange Multipliers Exercise 1 Exercise 3 Exercise 11 Exercise 19 Exercise 23 Exercise 33 Exercise 43 12 Multiple Integrals 12.1 Double Integrals over Rectangles Exercise 1 Exercise 7 Exercise 9a Exercise 13 Exercise 17 12.2 Iterated Integrals Exercise 3 Exercise 9 Exercise 13 Exercise 15 Exercise 19 Exercise 23 Exercise 31 12.3 Double Integrals over General Regions Exercise 5 Exercise 11 Exercise 15 Exercise 19 Exercise 37 Exercise 39 Exercise 45 Exercise 50 12.4 Double Integrals in Polar Coordinates Exercise 5 Exercise 13 Exercise 19 Exercise 23 Exercise 31 12.5 Applications of Double Integrals Exercise 1 Exercise 5 Exercise 13 Exercise 21 Exercise 23 12.6 Surface Area Exercise 3 Exercise 7 Exercise 11 Exercise 21 Exercise 23 12.7 Triple Integrals Exercise 9 Exercise 17 Exercise 21 Exercise 25 Exercise 33 Exercise 37 Exercise 47 12.8 Triple Integrals in Cylindrical and Spherical Coordinates Exercise 3 Exercise 7 Exercise 11 Exercise 17 Exercise 22 Exercise 27 12.9 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 Exercise 35 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 11 Exercise 15 Exercise 23 Exercise 27 Exercise 29 Exercise 33 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 Surface Integrals Exercise 4 Exercise 7 Exercise 15 Exercise 19 Exercise 25 Exercise 33 Exercise 41 13.7 Stokes' Theorem Exercise 1 Exercise 5 Exercise 7 Exercise 15 Exercise 19 13.8 The Divergence Theorem Exercise 1 Exercise 7 Exercise 9 Exercise 19 Exercise 25 Appendixes Appendix D Precise Definitions of Limits Exercise 15a Appendix G Integration of Rational Functions by Partial Fractions Exercise 5 Exercise 11 Exercise 17 Exercise 23 Exercise 27 Exercise 37 Appendix H.1 Polar Coordinates Exercise 11 Exercise 13 Exercise 19 Exercise 29 Exercise 33 Exercise 41 Exercise 45 Exercise 49 Exercise 51 Exercise 55 Appendix H.2 Polar Coordinates Exercise 7 Exercise 9 Exercise 17 Exercise 21 Exercise 25 Exercise 31 Exercise 37