Stewart Calculus
1 Functions and Models 1.1 Four Ways to Represent a Function Exercise 2 Exercise 9 Exercise 11 Exercise 15 Exercise 25 Exercise 33 Exercise 41 Exercise 45 Exercise 49 Exercise 57 Exercise 61 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 29a Exercise 35a Exercise 35d Exercise 46 Exercise 53 Exercise 63 1.4 Graphing Calculators and Computers Exercise 8 Exercise 9 Exercise 25 Exercise 29 Exercise 31 Exercise 35 1.5 Exponential Functions Exercise 9 Exercise 13 Exercise 15 Exercise 17 Exercise 21 Exercise 27 1.6 Inverse Functions and Logarithms Exercise 3 Exercise 6 Exercise 13 Exercise 17 Exercise 19 Exercise 22 Exercise 25 Exercise 45 Exercise 47 Exercise 51a Exercise 51b Exercise 61 1.7 Parametric Curves Exercise 4 Exercise 7 Exercise 11 Exercise 19 Exercise 29 Exercise 31 Exercise 32 Exercise 39 Exercise 43 Exercise 45 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 9 Exercise 15 Exercise 27 Exercise 32 2.3 Calculating Limits Using the Limit Laws Exercise 6 Exercise 13 Exercise 16 Exercise 17 Exercise 29 Exercise 33 Exercise 39 Exercise 47 Exercise 49 2.4 Continuity Exercise 3 Exercise 9 Exercise 13 Exercise 16 Exercise 23 Exercise 25 Exercise 28 Exercise 33 Exercise 35 Exercise 41 Exercise 47 Exercise 51 2.5 Limits Involving Infinity Exercise 2 Exercise 7 Exercise 15 Exercise 23 Exercise 27 Exercise 39 Exercise 51 2.6 Derivatives and Rates of Change Exercise 7 Exercise 9 Exercise 13 Exercise 17 Exercise 20 Exercise 21 Exercise 25 Exercise 29 Exercise 37 Exercise 41 Exercise 45 Exercise 47 Exercise 49 Exercise 53 2.7 The Derivative as a Function Exercise 3b Exercise 3c Exercise 5 Exercise 11 Exercise 17a Exercise 17b Exercise 25 Exercise 27 Exercise 35 Exercise 41 Exercise 47 Exercise 51 2.8 What Does f' Say about f? Exercise 5 Exercise 9 Exercise 13 Exercise 14 Exercise 15 Exercise 21 Exercise 29 3 Differentiation Rules 3.1 Derivatives of Polynomials and Exponential Functions Exercise 19 Exercise 25 Exercise 29 Exercise 42 Exercise 45 Exercise 48 Exercise 49 Exercise 57 Exercise 63 Exercise 69 Exercise 71 3.2 The Product and Quotient Rules Exercise 9 Exercise 23 Exercise 31 Exercise 34 Exercise 41 Exercise 43 Exercise 48 Exercise 51 Exercise 53 Exercise 57 3.3 Derivatives of Trigonometric Functions Exercise 9 Exercise 20 Exercise 27 Exercise 31 Exercise 33 Exercise 37 Exercise 39 Exercise 41 Exercise 43 Exercise 45 Exercise 49 3.4 The Chain Rule Exercise 5 Exercise 19 Exercise 21 Exercise 33 Exercise 45 Exercise 49 Exercise 51 Exercise 55 Exercise 59 Exercise 67 Exercise 69 Exercise 76 Exercise 81 Exercise 85a Exercise 85b Exercise 91 3.5 Implicit Differentiation Exercise 13 Exercise 25 Exercise 39 Exercise 43 Exercise 51 Exercise 55 3.6 Inverse Trigonometric Functions and their Derivatives Exercise 11 Exercise 19 Exercise 31 Exercise 39 Exercise 41a Exercise 41b 3.7 Derivatives of Logarithmic Functions Exercise 17 Exercise 23 Exercise 29 Exercise 37 Exercise 44 Exercise 47 3.8 Rates of Change in the Natural and Social Sciences Exercise 1g Exercise 1h Exercise 1i Exercise 21 Exercise 28 Exercise 31 Exercise 35 3.9 Linear Approximations and Differentials Exercise 13 Exercise 23 Exercise 25 Exercise 27 Exercise 33 Exercise 35 4 Applications of Differentiation 4.1 Related Rates Exercise 11 Exercise 15 Exercise 19 Exercise 29 Exercise 33 Exercise 37a Exercise 37b Exercise 43 4.2 Maximum and Minimum Values Exercise 9 Exercise 11 Exercise 13 Exercise 21 Exercise 33 Exercise 35 Exercise 43 Exercise 59 Exercise 66 4.3 Derivatives and the Shapes of Curves Exercise 5c Exercise 9a Exercise 9b Exercise 9c Exercise 15 Exercise 27 Exercise 29a Exercise 29b Exercise 29c Exercise 39 Exercise 39d Exercise 43 Exercise 59 Exercise 61 Exercise 63 Exercise 65 4.4 Graphing with Calculus and Calculators Exercise 11 Exercise 23 Exercise 25 Exercise 26 Exercise 30 Exercise 31 4.5 Indeterminate Forms and l'Hospital's Rule Exercise 1 Exercise 19 Exercise 31 Exercise 34 Exercise 41 Exercise 51 Exercise 55 Exercise 57 Exercise 63 Exercise 75 4.6 Optimization Problems Exercise 11 Exercise 13 Exercise 15 Exercise 20 Exercise 23 Exercise 25 Exercise 37 Exercise 39 Exercise 43 Exercise 45 Exercise 51 Exercise 57 4.7 Newton's Method Exercise 4 Exercise 18 Exercise 25 Exercise 29 Exercise 33 4.8 Antiderivatives Exercise 11 Exercise 17 Exercise 19 Exercise 31 Exercise 39 Exercise 41 Exercise 45 Exercise 51 Exercise 55 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 31 Exercise 35 Exercise 41 Exercise 43 Exercise 51 5.3 Evaluating Definite Integrals Exercise 7 Exercise 13 Exercise 29 Exercise 37 Exercise 40 Exercise 43 Exercise 50 Exercise 53 Exercise 59 Exercise 61 Exercise 74 5.4 The Fundamental Theorem of Calculus Exercise 3 Exercise 9 Exercise 13 Exercise 17 Exercise 19 Exercise 30 Exercise 31 5.5 The Substitution Rule Exercise 3 Exercise 13 Exercise 15 Exercise 19 Exercise 25 Exercise 35 Exercise 47 Exercise 52 Exercise 55 Exercise 61 Exercise 67 Exercise 71 5.6 Integration by Parts Exercise 3 Exercise 13 Exercise 16 Exercise 27 Exercise 39 Exercise 43 Exercise 46 5.7 Additional Techniques of Integration Exercise 3 Exercise 6 Exercise 11 Exercise 23 Exercise 25 Exercise 35 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 29 Exercise 31 Exercise 39 5.10 Improper Integrals Exercise 1 Exercise 7 Exercise 13 Exercise 19 Exercise 27 Exercise 31 Exercise 37 Exercise 43 Exercise 51 Exercise 53 Exercise 59 6 Applications of Integration 6.1 More about Areas Exercise 3 Exercise 9 Exercise 13 Exercise 23 Exercise 33 Exercise 39 Exercise 45 6.2 Volumes Exercise 5 Exercise 7 Exercise 9 Exercise 25b Exercise 31 Exercise 33 Exercise 39 Exercise 45 Exercise 49 6.3 Volumes by Cylindrical Shells Exercise 5 Exercise 11 Exercise 15 Exercise 19 Exercise 23a Exercise 31 Exercise 37 6.4 Arc Length Exercise 7 Exercise 9 Exercise 15 Exercise 23 Exercise 25 Exercise 29 Exercise 32 6.5 Average Value of a Function Exercise 5 Exercise 7 Exercise 11 Exercise 15 Exercise 21 6.6 Applications to Physics and Engineering Exercise 5 Exercise 7 Exercise 11 Exercise 15 Exercise 17 Exercise 25 Exercise 33 Exercise 37 Exercise 47 6.7 Applications to Economics and Biology Exercise 3 Exercise 5 Exercise 10 Exercise 17 6.8 Probability Exercise 1 Exercise 7 Exercise 8 Exercise 13 7 Differential Equations 7.1 Modeling with Differential Equations Exercise 3 Exercise 7 Exercise 9 Exercise 11 Exercise 15 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 10 Exercise 13 Exercise 25 Exercise 31 Exercise 39 Exercise 43 Exercise 49 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 9 Exercise 11 Exercise 15 Exercise 17 7.6 Predator-Prey Systems Exercise 1 Exercise 5 Exercise 7 Exercise 9 8 Infinite Sequences and Series 8.1 Sequences Exercise 3 Exercise 9 Exercise 11 Exercise 25 Exercise 31 Exercise 45 Exercise 49 Exercise 53 Exercise 55 8.2 Series Exercise 3 Exercise 9 Exercise 17 Exercise 27 Exercise 31 Exercise 37 Exercise 41 Exercise 47 Exercise 53 Exercise 59 Exercise 63 Exercise 65 8.3 The Integral and Comparison Tests; Estimating Sums Exercise 3 Exercise 13 Exercise 15 Exercise 17 Exercise 20 Exercise 22 Exercise 29 Exercise 33 Exercise 39 Exercise 41 8.4 Other Convergence Tests Exercise 3 Exercise 7 Exercise 13 Exercise 15 Exercise 21 Exercise 28 Exercise 29 Exercise 35 Exercise 37 Exercise 39 Exercise 41 8.5 Power Series Exercise 3 Exercise 7 Exercise 13 Exercise 19 Exercise 24 Exercise 25 Exercise 31 8.6 Representations of Functions as Power Series Exercise 5 Exercise 8 Exercise 11a Exercise 11b Exercise 13 Exercise 21 Exercise 23 Exercise 35 Exercise 37 8.7 Taylor and Maclaurin Series Exercise 5 Exercise 13 Exercise 23 Exercise 29 Exercise 31 Exercise 35 Exercise 41 Exercise 53 Exercise 55 Exercise 59 8.8 Applications of Taylor Polynomials Exercise 5 Exercise 7 Exercise 15 Exercise 16 Exercise 21 Exercise 27 Exercise 29 9 Vectors and the Geometry of Space 9.1 Three-Dimensional Coordinate Systems Exercise 5 Exercise 11 Exercise 19 Exercise 25 Exercise 31 Exercise 35 Exercise 39 9.2 Vectors Exercise 3 Exercise 9 Exercise 21 Exercise 23 Exercise 35 Exercise 39 Exercise 43 9.3 The Dot Product Exercise 11 Exercise 17 Exercise 25 Exercise 33 Exercise 35 Exercise 41 Exercise 43 Exercise 49 9.4 The Cross Product Exercise 1 Exercise 4 Exercise 13 Exercise 19 Exercise 23 Exercise 33 Exercise 35 Exercise 39 9.5 Equations of Lines and Planes Exercise 5 Exercise 7 Exercise 11 Exercise 17 Exercise 25 Exercise 39 Exercise 47 Exercise 59 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 21 Exercise 33 10 Vector Functions 10.1 Vector Functions and Space Curves Exercise 11 Exercise 21 Exercise 25 Exercise 37 Exercise 41 10.2 Derivatives and Integrals of Vector Functions Exercise 1 Exercise 3 Exercise 13 Exercise 17 Exercise 23 Exercise 51 10.3 Arc Length and Curvature Exercise 3 Exercise 5 Exercise 17 Exercise 31 Exercise 33 Exercise 37 Exercise 45 Exercise 51 Exercise 55 10.4 Motion in Space: Velocity and Acceleration Exercise 9 Exercise 17 Exercise 20 Exercise 23 Exercise 35 10.5 Parametric Surfaces Exercise 3 Exercise 13 Exercise 19 Exercise 23 Exercise 26 Exercise 31 11 Partial Derivatives 11.1 Functions of Several Variables Exercise 1 Exercise 5 Exercise 13 Exercise 23 Exercise 35 Exercise 41 Exercise 45 11.2 Limits and Continuity Exercise 7 Exercise 11 Exercise 19 Exercise 23 Exercise 26 Exercise 33 Exercise 35 11.3 Partial Derivatives Exercise 1 Exercise 5a Exercise 5b Exercise 9 Exercise 21 Exercise 31 Exercise 50 Exercise 67 Exercise 79 Exercise 84 Exercise 85 11.4 Tangent Planes and Linear Approximations Exercise 11 Exercise 19 Exercise 29 Exercise 33 Exercise 39 Exercise 45 Exercise 47 11.5 The Chain Rule Exercise 5 Exercise 11 Exercise 17 Exercise 30 Exercise 33 Exercise 37 Exercise 43 Exercise 45 11.6 Directional Derivatives and the Gradient Vector Exercise 1 Exercise 11 Exercise 19 Exercise 21 Exercise 25 Exercise 27 Exercise 31 Exercise 43 Exercise 55 Exercise 61 11.7 Maximum and Minimum Values Exercise 1 Exercise 3 Exercise 11 Exercise 29 Exercise 37 Exercise 39 Exercise 47 11.8 Lagrange Multipliers Exercise 1 Exercise 3 Exercise 11 Exercise 19 Exercise 25 Exercise 35 Exercise 45 12 Multiple Integrals 12.1 Double Integrals over Rectangles Exercise 1 Exercise 7 Exercise 9a Exercise 9b Exercise 13 Exercise 17 12.2 Iterated Integrals Exercise 3 Exercise 9 Exercise 17 Exercise 19 Exercise 23 Exercise 27 Exercise 35 12.3 Double Integrals over General Regions Exercise 5 Exercise 17 Exercise 21 Exercise 25 Exercise 45 Exercise 47 Exercise 53 Exercise 60 12.4 Double Integrals in Polar Coordinates Exercise 1 Exercise 11 Exercise 13 Exercise 21 Exercise 25 Exercise 35 12.5 Applications of Double Integrals Exercise 1 Exercise 5 Exercise 15 Exercise 23 Exercise 25 12.6 Surface Area Exercise 3 Exercise 7 Exercise 9 Exercise 21 Exercise 27 12.7 Triple Integrals Exercise 11 Exercise 19 Exercise 23 Exercise 27 Exercise 35 Exercise 39 Exercise 51 12.8 Triple Integrals in Cylindrical and Spherical Coordinates Exercise 3 Exercise 7 Exercise 11 Exercise 17 Exercise 26 Exercise 31 12.9 Change of Variables in Multiple Integrals Exercise 7 Exercise 17 Exercise 25 13 Vector Calculus 13.1 Vector Fields Exercise 5 Exercise 11 Exercise 17 Exercise 23 Exercise 29 Exercise 35 13.2 Line Integrals Exercise 3 Exercise 7 Exercise 11 Exercise 17 Exercise 21 Exercise 33 Exercise 39 Exercise 43 13.3 The Fundamental Theorem for Line Integrals Exercise 7 Exercise 11 Exercise 15 Exercise 25 Exercise 29 Exercise 35 13.4 Green's Theorem Exercise 3 Exercise 7 Exercise 9 Exercise 17 Exercise 21 Exercise 29 13.5 Curl and Divergence Exercise 1 Exercise 11 Exercise 15 Exercise 19 Exercise 21 Exercise 31 13.6 Surface Integrals Exercise 4 Exercise 9 Exercise 17 Exercise 21 Exercise 27 Exercise 37 Exercise 45 13.7 Stokes' Theorem Exercise 1 Exercise 5 Exercise 7 Exercise 15 Exercise 19 13.8 The Divergence Theorem Exercise 1 Exercise 7 Exercise 19 Exercise 25 Appendixes Appendix D Precise Definitions of Limits Exercise 3 Exercise 15 Exercise 19a Appendix G Integration of Rational Functions by Partial Fractions Exercise 5 Exercise 11 Exercise 17 Exercise 23 Exercise 27 Exercise 29 Exercise 37 Appendix H.1 Curves in Polar Coordinates Exercise 11 Exercise 13 Exercise 19 Exercise 29 Exercise 33 Exercise 43 Exercise 47 Exercise 49 Exercise 53 Exercise 57 Appendix H.2 Area and Lengths in Polar Coordinates Exercise 7 Exercise 9 Exercise 17 Exercise 21 Exercise 25 Exercise 31 Exercise 37