Stewart Calculus
1 Functions and Limits 1.1 Four Ways to Represent a Function Exercise 4 Exercise 11 Exercise 13 Exercise 17 Exercise 27 Exercise 35 Exercise 45 Exercise 49 Exercise 53 Exercise 61 Exercise 67 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 The Tangent and Velocity Problems Exercise 3 Exercise 5 Exercise 9 1.5 The Limit of a Function Exercise 5 Exercise 13 Exercise 17 Exercise 31 Exercise 46 1.6 Calculating Limits Using the Limit Laws Exercise 6 Exercise 15 Exercise 18 Exercise 19 Exercise 37 Exercise 41 Exercise 51 Exercise 60 Exercise 63 1.7 The Precise Definition of a Limit Exercise 3 Exercise 17 Exercise 25 Exercise 29 Exercise 31 Exercise 37 Exercise 43 1.8 Continuity Exercise 3 Exercise 9 Exercise 13 Exercise 20 Exercise 36 Exercise 43 Exercise 45 Exercise 51 Exercise 65 2 Derivatives 2.1 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 53 2.2 The Derivative as a Function Exercise 3b Exercise 3c Exercise 5 Exercise 11 Exercise 17a Exercise 17b Exercise 27 Exercise 33 Exercise 35 Exercise 41 Exercise 47 Exercise 51 Exercise 53 2.3 Differentiation Formulas Exercise 10 Exercise 17 Exercise 27 Exercise 43 Exercise 54 Exercise 55 Exercise 60 Exercise 63 Exercise 67 Exercise 74 Exercise 75 Exercise 83 Exercise 85 Exercise 97 2.4 Derivatives of Trigonometric Functions Exercise 9 Exercise 29 Exercise 33 Exercise 37 Exercise 41 Exercise 45 Exercise 49 Exercise 51 Exercise 55 2.5 The Chain Rule Exercise 5 Exercise 17 Exercise 37 Exercise 59 Exercise 61 Exercise 65 Exercise 73 Exercise 75 Exercise 80 Exercise 87 2.6 Implicit Differentiation Exercise 15 Exercise 29 Exercise 43 Exercise 51 Exercise 57 Exercise 61 2.7 Rates of Change in the Natural and Social Sciences Exercise 1g Exercise 1h Exercise 1i Exercise 15 Exercise 19 Exercise 23 Exercise 28 Exercise 31 Exercise 35 2.8 Related Rates Exercise 12 Exercise 15 Exercise 19 Exercise 25 Exercise 27 Exercise 33 Exercise 39a Exercise 39b Exercise 45 2.9 Linear Approximations and Differentials Exercise 3 Exercise 5 Exercise 9 Exercise 13 Exercise 29 Exercise 31 Exercise 38 Exercise 41 3 Applications of Differentiation 3.1 Maximum and Minimum Values Exercise 9 Exercise 11 Exercise 13 Exercise 25 Exercise 39 Exercise 41 Exercise 47 Exercise 61 Exercise 72 3.2 The Mean Value Theorem Exercise 5 Exercise 9 Exercise 19 Exercise 23 Exercise 25 Exercise 33 3.3 How Derivatives Affect the Shape of a Graph Exercise 5a Exercise 5b Exercise 7c 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 61 3.4 Limits at Infinity; Horizontal Asymptotes Exercise 2 Exercise 13 Exercise 19 Exercise 35 Exercise 53 Exercise 59 Exercise 61 Exercise 67a Exercise 67b 3.5 Summary of Curve Sketching Exercise 5 Exercise 9 Exercise 19 Exercise 35 Exercise 45 3.6 Graphing with Calculus and Calculators Exercise 11 Exercise 23 3.7 Optimization Problems Exercise 15 Exercise 18 Exercise 19 Exercise 21 Exercise 24 Exercise 32 Exercise 35 Exercise 51 Exercise 52 Exercise 57b Exercise 59 Exercise 67 3.8 Newton's Method Exercise 4 Exercise 29 Exercise 35 Exercise 39 3.9 Antiderivatives Exercise 13 Exercise 19 Exercise 21 Exercise 35 Exercise 43 Exercise 47 Exercise 51 Exercise 59 Exercise 67 4 Integrals 4.1 Areas and Distances Exercise 2 Exercise 5 Exercise 13 Exercise 17 Exercise 23 4.2 The Definite Integral Exercise 5 Exercise 9 Exercise 19 Exercise 23 Exercise 33 Exercise 37 Exercise 47 Exercise 49 Exercise 57 4.3 The Fundamental Theorem of Calculus Exercise 3 Exercise 9 Exercise 13 Exercise 47 Exercise 49 Exercise 58 Exercise 59 Exercise 68 Exercise 69 4.4 Indefinite Integrals and the Net Change Theorem Exercise 2 Exercise 9 Exercise 41 Exercise 46 Exercise 49 Exercise 55 Exercise 57 Exercise 72 4.5 The Substitution Rule Exercise 3 Exercise 25 Exercise 44 Exercise 59 Exercise 63 Exercise 67 Exercise 69 Exercise 71 Exercise 75 Exercise 81 5 Applications of Integration 5.1 Areas Between Curves Exercise 11 Exercise 13 Exercise 29 Exercise 47 Exercise 53 Exercise 55 Exercise 58 5.2 Volumes Exercise 7 Exercise 9 Exercise 11 Exercise 41 Exercise 47 Exercise 49 Exercise 55 Exercise 61 Exercise 65 5.3 Volumes by Cylindrical Shells Exercise 13 Exercise 17 Exercise 25a Exercise 29 Exercise 41 Exercise 47 5.4 Work Exercise 7 Exercise 9 Exercise 13 Exercise 17 Exercise 19 Exercise 27 5.5 Average Value of a Function Exercise 7 Exercise 9 Exercise 13 Exercise 17 Exercise 23 6 Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions 6.1 Inverse Functions Exercise 3 Exercise 6 Exercise 15 Exercise 19 Exercise 21 Exercise 24 Exercise 41 Exercise 43 6.2 Exponential Functions and Their Derivatives Exercise 5 Exercise 9 Exercise 11 Exercise 13 Exercise 17 Exercise 21 Exercise 35 Exercise 41 Exercise 53 Exercise 59 Exercise 71 Exercise 73 Exercise 83 Exercise 89 Exercise 94 6.2* The Natural Logarithmic Function Exercise 25 Exercise 39 Exercise 47 Exercise 70 Exercise 71 Exercise 89 6.3 Logarithmic Functions Exercise 23 Exercise 29a Exercise 29b Exercise 36 Exercise 41 Exercise 49 Exercise 61 6.3* The Natural Exponential Function Exercise 7b Exercise 12 Exercise 19 Exercise 25 Exercise 37 Exercise 43 Exercise 54 Exercise 55 Exercise 61 Exercise 73 Exercise 75 Exercise 85 Exercise 91 Exercise 96 6.4 Derivatives of Logarithmic Functions Exercise 21 Exercise 31 Exercise 47 Exercise 49 Exercise 56 Exercise 61 Exercise 77 Exercise 93 6.4* General Logarithmic and Exponential Functions Exercise 12 Exercise 17 Exercise 37 Exercise 45 Exercise 49 Exercise 54 6.5 Exponential Growth and Decay Exercise 3 Exercise 5 Exercise 9 Exercise 13 Exercise 19 6.6 Inverse Trigonometric Functions Exercise 13 Exercise 25 Exercise 37 Exercise 45 Exercise 47 Exercise 63 6.7 Hyperbolic Functions Exercise 9 Exercise 15 Exercise 17 Exercise 35 Exercise 43 Exercise 51 Exercise 55 6.8 Indeterminate Forms and l'Hospital's Rule Exercise 1 Exercise 25 Exercise 45 Exercise 50 Exercise 57 Exercise 71 Exercise 75 Exercise 83 Exercise 99 7 Techniques of Integration 7.1 Integration by Parts Exercise 3 Exercise 15 Exercise 17 Exercise 24 Exercise 39 Exercise 51 Exercise 61 Exercise 67 Exercise 70 7.2 Trigonometric Integrals Exercise 3 Exercise 7 Exercise 11 Exercise 23 Exercise 29 Exercise 41 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 6 Exercise 11 Exercise 17 Exercise 23 Exercise 29 Exercise 31 Exercise 43 Exercise 47 Exercise 57 7.5 Strategy for Integration Exercise 7 Exercise 17 Exercise 23 Exercise 31 Exercise 41 Exercise 45 Exercise 49 Exercise 57 Exercise 63 Exercise 71 7.6 Integration Using Tables and Computer Algebra Systems Exercise 10 Exercise 17 Exercise 19 Exercise 26 Exercise 29 Exercise 31 Exercise 35 7.7 Approximate Integration Exercise 1 Exercise 3 Exercise 4 Exercise 35 Exercise 37 Exercise 47 7.8 Improper Integrals Exercise 1 Exercise 7 Exercise 13 Exercise 21 Exercise 29 Exercise 31 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 part i Exercise 1a part ii 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 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 15 9.2 Direction Fields and Euler's Method Exercise 3 Exercise 11 Exercise 13 Exercise 18 Exercise 19 Exercise 21 Exercise 23 9.3 Separable Equations Exercise 10 Exercise 13 Exercise 25 Exercise 31 Exercise 39 Exercise 43 Exercise 49 9.4 Models for Population Growth Exercise 1 Exercise 3 Exercise 9 Exercise 11 Exercise 16 Exercise 17 Exercise 19 9.5 Linear Equations Exercise 7 Exercise 9 Exercise 19 Exercise 25 Exercise 31 Exercise 33 9.6 Predator-Prey Systems Exercise 1 Exercise 5 Exercise 7 Exercise 9 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 51 10.2 Calculus with Parametric Curves Exercise 5 Exercise 11 Exercise 23 Exercise 25 Exercise 31 Exercise 41 Exercise 45 Exercise 63 Exercise 65 10.3 Polar Coordinates Exercise 11 Exercise 17 Exercise 25 Exercise 33 Exercise 37 Exercise 47 Exercise 53 Exercise 57 Exercise 61 Exercise 65 10.4 Areas and Lengths in Polar Coordinates Exercise 7 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 1 Exercise 13 Exercise 13b Exercise 13c Exercise 13d Exercise 21 Exercise 27 (SV AP*) 10 Curves in Parametric, Vector, and Polar Form (SV AP*) 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 51 (SV AP*) 10.2 Calculus with Parametric Curves Exercise 23 Exercise 25 Exercise 31 Exercise 41 Exercise 45 Exercise 63 Exercise 65 (SV AP*) 10.3 Vectors in Two Dimensions Exercise 31 Exercise 45 Exercise 51 (SV AP*) 10.4 Vector Functions and Their Derivatives Exercise 21 Exercise 31 (SV AP*) 10.5 Curvilinear Motion: Velocity and Acceleration Exercise 21 (SV AP*) 10.6 Polar Coordinates Exercise 11 Exercise 25 Exercise 33 Exercise 37 Exercise 47 Exercise 53 Exercise 57 Exercise 61 Exercise 65 (SV AP*) 10.7 Areas and Lengths in Polar Coordinates Exercise 7 Exercise 21 Exercise 27 Exercise 31 Exercise 41 Exercise 47 (SV AP*) 10.8 Conic Sections Exercise 5 Exercise 15 Exercise 27 Exercise 33 Exercise 37 Exercise 47 (SV AP*) 10.9 Conic Sections in Polar Coordinates Exercise 13 Exercise 13b Exercise 13c Exercise 13d Exercise 21 Exercise 27 11 Infinite Sequences and Series 11.1 Sequences Exercise 17 Exercise 25 Exercise 42 Exercise 43 Exercise 53 Exercise 64 Exercise 71 Exercise 73 Exercise 81 11.2 Series Exercise 9 Exercise 15 Exercise 23 Exercise 39 Exercise 43 Exercise 51 Exercise 57 Exercise 67 Exercise 73 Exercise 79 Exercise 85 Exercise 87 11.3 The Integral Test and Estimates of Sums Exercise 7 Exercise 11 Exercise 17 Exercise 21 Exercise 37 Exercise 43 11.4 The Comparison Tests Exercise 1 Exercise 5 Exercise 7 Exercise 17 Exercise 31 Exercise 37 Exercise 41 11.5 Alternating Series Exercise 3 Exercise 7 Exercise 11 Exercise 17 Exercise 23 Exercise 32 11.6 Absolute Convergence and the Ratio and Root Tests Exercise 3 Exercise 13 Exercise 19 Exercise 21 Exercise 31 Exercise 35 Exercise 37 11.8 Power Series Exercise 5 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 23 Exercise 25 Exercise 37 Exercise 39 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 33 Exercise 37 Exercise 41 12.2 Vectors Exercise 3 Exercise 13 Exercise 25 Exercise 29 Exercise 45 Exercise 47 Exercise 51 12.3 The Dot Product Exercise 11 Exercise 19 Exercise 27 Exercise 45 Exercise 47 Exercise 53 Exercise 55 Exercise 61 12.4 The Cross Product Exercise 7 Exercise 13 Exercise 16 Exercise 19 Exercise 31 Exercise 45 Exercise 49 Exercise 53 12.5 Equations of Lines and Planes Exercise 5 Exercise 7 Exercise 13 Exercise 19 Exercise 31 Exercise 51 Exercise 63 Exercise 75 12.6 Cylinders and Quadric Surfaces Exercise 9 Exercise 19 13 Vector Functions 13.1 Vector Functions and Space Curves Exercise 13 Exercise 23 Exercise 27 Exercise 41 Exercise 45 13.2 Derivatives and Integrals of Vector Functions Exercise 1 Exercise 3 Exercise 15 Exercise 19 Exercise 25 Exercise 53 13.3 Arc Length and Curvature Exercise 3 Exercise 5 Exercise 17 Exercise 31 Exercise 33 Exercise 39 Exercise 47 Exercise 53 Exercise 57 13.4 Motion in Space: Velocity and Acceleration Exercise 11 Exercise 19 Exercise 22 Exercise 25 Exercise 39 14 Partial Derivatives 14.1 Functions of Several Variables Exercise 1 Exercise 7 Exercise 15 Exercise 19 Exercise 25 Exercise 32 Exercise 37 Exercise 47 Exercise 59 Exercise 65 Exercise 69 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 9 Exercise 21 Exercise 33 Exercise 52 Exercise 73 Exercise 83 Exercise 92 Exercise 93 14.4 Tangent Planes and Linear Approximations Exercise 11 Exercise 21 Exercise 31 Exercise 35 Exercise 43 Exercise 45 14.5 The Chain Rule Exercise 5 Exercise 11 Exercise 17 Exercise 35 Exercise 39 Exercise 45 Exercise 47 14.6 Directional Derivatives and the Gradient Vector Exercise 1 Exercise 11 Exercise 19 Exercise 23 Exercise 27 Exercise 29 Exercise 33 Exercise 41 Exercise 61 Exercise 67 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 21 Exercise 27 Exercise 37 Exercise 47 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 17 Exercise 21 Exercise 25 Exercise 47 Exercise 49 Exercise 55 Exercise 62 15.4 Double Integrals in Polar Coordinates Exercise 1 Exercise 11 Exercise 13 Exercise 15 Exercise 25 Exercise 39 15.5 Applications of Double Integrals Exercise 5 Exercise 15 Exercise 27 Exercise 29 15.6 Surface Area Exercise 3 Exercise 9 Exercise 12 15.7 Triple Integrals Exercise 13 Exercise 19 Exercise 23 Exercise 27 Exercise 35 Exercise 41 Exercise 53 15.8 Triple Integrals in Cylindrical Coordinates Exercise 9 Exercise 17 Exercise 21 15.9 Triple Integrals in Spherical Coordinates Exercise 5 Exercise 17 Exercise 21 Exercise 30 Exercise 35 15.10 Change of Variables in Multiple Integrals Exercise 7 Exercise 17 Exercise 25 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 45 16.3 The Fundamental Theorem for Line Integrals Exercise 7 Exercise 11 Exercise 15 Exercise 25 Exercise 29 Exercise 35 16.4 Green's Theorem Exercise 3 Exercise 7 Exercise 9 Exercise 17 Exercise 21 Exercise 29 16.5 Curl and Divergence Exercise 11 Exercise 13 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 39 Exercise 45 Exercise 49 Exercise 59 Exercise 61 16.7 Surface Integrals Exercise 4 Exercise 9 Exercise 17 Exercise 23 Exercise 27 Exercise 39 Exercise 47 16.8 Stokes' Theorem Exercise 1 Exercise 5 Exercise 7 Exercise 15 Exercise 19 16.9 The Divergence Theorem Exercise 1 Exercise 7 Exercise 19 Exercise 25 17 Second-Order Differential Equations 17.1 Second-Order Linear Equations Exercise 1 Exercise 9 Exercise 11 Exercise 19 Exercise 31 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 : Graphing Calculators and Computers Exercise 8 Exercise 9 Exercise 25 Exercise 29 Exercise 31 Exercise 35