# Stewart Calculus, 8th Edition Stewart Calculus, 8th Edition

8th Edition | ISBN: 9781285740621 / 1285740629

10,702

expert-verified solutions in this book

8th Edition | ISBN: 9781285740621 / 1285740629

10,702

expert-verified solutions in this book

### Chapter 1

Functions And Limits

 1.1 Four Ways to Represent a Function Exercises p.19 1.2 Mathematical Models: A Catalog of Essential Functions Exercises p.33 1.3 New Functions from Old Functions Exercises p.42 1.4 The Tangent and Velocity Problems Exercises p.49 1.5 The Limit of a Function Exercises p.59 1.6 Calculating Limits Using the Limit Laws Exercises p.70 1.7 The Precise Definition of a Limit Exercises p.81 1.8 Continuity Exercises p.91 Concept Check p.94 True-False Quiz p.95 Review Exercises p.96 Problem Solving p.102

### Chapter 2

Derivatives

 2.1 Derivatives and Rates of Change Exercises p.113 2.2 The Derivative as a Function Exercises p.125 2.3 Differentiation Formulas Exercises p.140 2.4 Derivatives of Trigonometric Functions Exercises p.150 2.5 The Chain Rule Exercises p.158 2.6 Implicit Differentiation Exercises p.166 2.7 Rates of Change in the Natural and Social Sciences Exercises p.178 2.8 Related Rates Exercises p.185 2.9 Linear Aproximations and Differentials Exercises p.192 Concept Check p.195 True-False Quiz p.196 Review Exercises p.196 Problems Plus p.200

### Chapter 3

Applications Of Differentiation

 3.1 Maximum and Minimum Values Exercises p.211 3.2 The Mean Value Theorem Exercises p.219 3.3 How Derivatives Affect the Shape of a Graph Exercises p.227 3.4 Limits at Infinity; Horizontal Asymptotes Exercises p.241 3.5 Summary of Curve Sketching Exercises p.250 3.6 Graphing with Calculus and Calculators Exercises p.257 3.7 Optimization Problems Exercises p.264 3.8 Newton's Method Exercises p.276 3.9 Antiderivatives Exercises p.282 Concept Check p.285 True-False Quiz p.285 Review Exercises p.286 Problems Plus p.290

### Chapter 4

Integrals

 4.1 Areas and Distances Exercises p.303 4.2 The Definite Integral Exercises p.316 4.3 The Fundamental Theorem of Calculus Exercises p.327 4.4 Indefinite Integrals and the Net Change Theorem Exercises p.336 4.5 The Substitution Rule Exercises p.346 Concept Check p.348 True-False Quiz p.348 Review Exercises p.349 Problems Plus p.353

### Chapter 5

Applications Of Integration

 5.1 Areas Between Curves Exercises p.362 5.2 Volumes Exercises p.374 5.3 Volumes by Cylindrical Shells Exercises p.381 5.4 Work Exercises p.386 5.5 Average Value of a Function Exercises p.391 Concept Check p.393 Review Exercises p.393 Problems Plus p.395

### Chapter 6

Inverse Functions

 6.1 Inverse Functions Exercises p.406 6.2 Exponential Functions and Their Derivatives Exercises p.418 6.3 Logarithmic Functions Exercises p.426 6.4 Derivatives of Logarithmic Functions Exercises p.436 6.2* The Natural Logarithmic Function Exercises p.445 6.3* The Natural Exponential Function Exercises p.452 6.4* General Logarithmic and Exponential Functions Exercises p.463 6.5 Exponential Growth and Decay Exercises p.471 6.6 Inverse Trigonometric Functions Exercises p.481 6.7 Hyperbolic Functions Exercises p.489 6.8 Indeterminate Forms and l'Hospital's Rule Exercises p.499 Concept Check p.503 True-False Quiz p.504 Review Exercises p.505 Problems Plus p.509

### Chapter 7

Techniques Of Integration

 7.1 Integration by Parts Exercises p.516 7.2 Trigonometric Integrals Exercises p.524 7.3 Trigonometric Substitution Exercises p.531 7.4 Integration of Rational Functions by Partial Fractions Exercises p.541 7.5 Strategy for Integration Exercises p.547 7.6 Integration Using Tables and Computer Algebra Systems Exercises p.552 7.7 Approximate Integration Exercises p.564 7.8 Improper Integrals Exercises p.574 Review: Concept Check p.577 Review: True-False Quiz p.577 Review: Exercises p.577 Problems Plus p.581

### Chapter 8

Further Applications Of Integration

 8.1 Arc Length Exercises p.588 8.2 Area of a Surface of Revolution Exercises p.595 8.3 Applications to Physics and Engineering Exercises p.605 8.4 Applications to Economics and Biology Exercises p.612 8.5 Probability Exercises p.619 Review: Concept Check p.621 Review: Exercises p.621 Problems Plus p.623

### Chapter 9

Differential Equations

 9.1 Modeling with Differential Equations Exercises p.630 9.2 Direction Fields and Euler's Method Exercises p.637 9.3 Separable Equations Exercises p.645 9.4 Models for Population Growth Exercises p.657 9.5 Linear Equations Exercises p.665 9.6 Predator-Prey Systems Exercises p.671 Review: Concept Check p.674 Review: True-False Quiz p.674 Review: Exercises p.674 Problems Plus p.677

### Chapter 10

Parametric Equations And Polar Coordinates

 10.1 Curves Defined by Parametric Equations Exercises p.685 10.2 Calculus with Parametric Curves Exercises p.695 10.3 Polar Coordinates Exercises p.706 10.4 Areas and Lengths in Polar Coordinates Exercises p.712 10.5 Conic Sections Exercises p.720 10.6 Conic Sections in Polar Coordinates Exercises p.728 Review: Concept Check p.729 Review: True-False Quiz p.729 Review: Exercises p.730 Problems Plus p.732

### Chapter 11

Infinite Sequences And Series

 11.1 Sequences Exercises p.744 11.2 Series Exercises p.755 11.3 The Integral Test and Estimates of Sums Exercises p.765 11.4 The Comparison Tests Exercises p.771 11.5 Alternating Series Exercises p.776 11.6 Absolute Convergence and the Ratio and Root Tests Exercises p.782 11.7 Strategy for Testing Series Exercises p.786 11.8 Power Series Exercises p.791 11.9 Representations of Functions as Power Series Exercises p.797 11.10 Taylor and Maclaurin Series Exercises p.811 11.11 Applications of Taylor Polynomials Exercises p.820 Review: Concept Check p.824 Review: True-False Quiz p.824 Review: Exercises p.825 Problems Plus p.827

### Chapter 12

Vectors And The Geometry Of Space

 12.1 Three-Dimensional Coordinate Systems Exercises p.836 12.2 Vectors Exercises p.845 12.3 The Dot Product Exercises p.852 12.4 The Cross Product Exercises p.861 12.5 Equations of Lines and Planes Exercises p.871 12.6 Cylinders and Quadric Surfaces Exercises p.879 Review: Concept Check p.881 Review: True-False Quiz p.882 Review: Exercises p.882 Problems Plus p.884

### Chapter 13

Vector Functions

 13.1 Vector Functions and Space Curves Exercises p.893 13.2 Derivatives and Integrals of Vector Functions Exercises p.900 13.3 Arc Length and Curvature Exercises p.908 13.4 Motion in Space: Velocity and Acceleration Exercises p.918 Review: Concept Check p.921 Review: True-False Quiz p.921 Review: Exercises p.922 Problems Plus p.924

### Chapter 14

Partial Derivatives

 14.1 Functions of Several Variables Exercises p.939 14.2 Limits and Continuity Exercises p.950 14.3 Partial Derivatives Exercises p.963 14.4 Tangent Planes and Linear Approximations Exercises p.974 14.5 The Chain Rule Exercises p.983 14.6 Directional Derivatives and the Gradient Vector Exercises p.996 14.7 Maximum and Minimum Values Exercises p.1007 14.8 Lagrange Multipliers Exercises p.1017 Review: Concept Check p.1021 Review: True-False Quiz p.1022 Review: Exercises p.1022 Problems Plus p.1025

### Chapter 15

Multiple Integrals

 15.1 Double Integrals over Rectangles Exercises p.1039 15.2 Double Integrals over General Regions Exercises p.1048 15.3 Double Integrals in Polar Coordinates Exercises p.1054 15.4 Applications of Double Integrals Exercises p.1064 15.5 Surface Area Exercises p.1068 15.6 Triple Integrals Exercises p.1077 15.7 Triple Integrals in Cylindrical Coordinates Exercises p.1083 15.8 Triple Integrals in Spherical Coordinates Exercises p.1089 15.9 Change of Variables in Multiple Integrals Exercises p.1100 Review: Concept Check p.1101 Review: True-False Quiz p.1101 Review: Exercises p.1102 Problems Plus p.1105

### Chapter 16

Vector Calculus

 16.1 Vector Fields Exercises p.1113 16.2 Line Integrals Exercises p.1124 16.3 The Fundamental Theorem for Line Integrals Exercises p.1134 16.4 Green's Theorem Exercises p.1141 16.5 Curl and Divergence Exercises p.1149 16.6 Parametric Surfaces and Their Areas Exercises p.1160 16.7 Surface Integrals Exercises p.1172 16.8 Stoke's Theorem Exercises p.1179 16.9 The Divergence Theorem Exercise p.1185 Review: Concept Check p.1188 Review: True-False Quiz p.1188 Review: Exercises p.1189 Problems Plus p.1191

### Chapter 17

Second-Order Differential Equations

 17.1 Second-Order Linear Equations Exercises p.1200 17.2 Nonhomogeneous Linear Equations Exercises p.1207 17.3 Applications of Second-Order Differential Equations Exercises p.1215 17.4 Series Solutions Exercises p.1220 Review: Concept Check p.1221 Review: True-False Quiz p.1221 Review: Exercises p.1221