# Calculus, 9th Edition Calculus, 9th Edition 9th Edition | ISBN: 9781337624183 / 1337624187

10,688

expert-verified solutions in this book  9th Edition | ISBN: 9781337624183 / 1337624187

10,688

expert-verified solutions in this book

## Table of Contents

### Chapter 1

Functions And Limits

 1.1 Four Ways to Represent a Function Exercises p.17 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.50 1.5 The Limit of a Function Exercises p.60 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.92 Concept Check p.95 True-False Quiz p.95 Review Exercises p.96 Problems p.104

### Chapter 2

Derivatives

 2.1 Derivatives and Rates of Change Exercises p.116 2.2 The Derivative as a Function Exercises p.128 2.3 Differentiation Formulas Exercises p.143 2.4 Derivatives of Trigonometric Functions Exercises p.154 2.5 The Chain Rule Exercises p.162 2.6 Implicit Differentiation Exercises p.169 2.7 Rates of Change in the Natural and Social Sciences Exercises p.181 2.8 Related Rates Exercises p.189 2.9 Linear Approximations and Differentials Exercises p.196 Concept Check p.199 True-False Quiz p.200 Review Exercises p.200 Problems p.204

### Chapter 3

Applications Of Differentiation

 3.1 Maximum and Minimum Values Exercises p.216 3.2 The Mean Value Theorem Exercises p.225 3.3 What Derivatives Tell Us about the Shape of a Graph Exercises p.234 3.4 Limits at Infinity: Horizontal Asymptotes Exercises p.247 3.5 Summary of Curve Sketching Exercises p.256 3.6 Graphing with Calculus and Technology Exercises p.263 3.7 Optimization Problems Exercises p.270 3.8 Newton's Method Exercises p.283 3.9 Antiderivatives Exercises p.290 Concept Check p.292 True-False Quiz p.293 Review Exercises p.293 Problems p.298

### Chapter 4

Integrals

 4.1 The Area and Distance Problems Exercises p.311 4.2 The Definite Integral Exercises p.324 4.3 The Fundamental Theorem of Calculus Exercises p.335 4.4 Indefinite Integrals and the Net Change Theorem Exercises p.345 4.5 The Substitution Rule Exercises p.355 Concept Check p.357 True-False Quiz p.357 Review Exercises p.358 Problems p.361

### Chapter 5

Applications Of Integration

 5.1 Areas Between Curves Exercises p.370 5.2 Volumes Exercises p.384 5.3 Volumes by Cylindrical Shells Exercises p.392 5.4 Work Exercises p.398 5.5 Average Value of a Function Exercises p.403 Concept Check p.405 True-False Quiz p.406 Review Exercises p.406 Problems p.408

### Chapter 6

Inverse Functions

 6.1 Inverse Functions and Their Derivatives Exercises p.418 6.2 Exponential Functions and Their Derivatives Exercises p.429 6.3 Logarithmic Functions Exercises p.438 6.4 Derivatives of Logarithmic Functions Exercises p.448 6.2* The Natural Logarithmic Function Exercises p.458 6.3* The Natural Exponential Function Exercises p.465 6.4* General Logarithmic and Exponential Functions Exercises p.476 6.5 Exponential Growth and Decay Exercises p.484 6.6 Inverse Trigonometric Functions Exercises p.493 6.7 Hyperbolic Functions Exercises p.501 6.8 Indeterminate Forms and L'Hospital's Rule Exercises p.511 Concept Check p.516 True-False Quiz p.516 Review Exercises p.517 Problems p.521

### Chapter 7

Techniques Of Integration

 7.1 Integration by Parts Exercises p.528 7.2 Trigonometric Integrals Exercises p.536 7.3 Trigonometric Substitution Exercises p.543 7.4 Integration of Rational Functions by Partial Fractions Exercises p.553 7.5 Strategy for Integration Exercises p.559 7.6 Integration Using Tables and Technology Exercises p.565 7.7 Approximate Integration Exercises p.577 7.8 Improper Integrals Exercises p.587 Concept Check p.590 True-False Quiz p.591 Review Exercises p.591 Problems p.595

### Chapter 8

Further Applications Of Integration

 8.1 Arc Length Exercises p.603 8.2 Area of a Surface of Revolution Exercises p.611 8.3 Applications to Physics and Engineering Exercises p.622 8.4 Applications to Economics and Biology Exercises p.628 8.5 Probability Exercises p.636 Concept Check p.638 True-False Quiz p.638 Review Exercises p.638 Problems p.640

### Chapter 9

Differential Equations

 9.1 Modeling with Differential Equations Exercises p.648 9.2 Direction Fields and Euler's Method Exercises p.657 9.3 Separable Equations Exercises p.664 9.4 Models for Population Growth Exercises p.676 9.5 Linear Equations Exercises p.684 9.6 Predator-Prey Systems Exercises p.691 Concept Check p.694 True-False Quiz p.694 Review Exercises p.694 Problems p.697

### Chapter 10

Parametric Equations And Polar Coordinates

 10.1 Curves Defined by Parametric Equations Exercises p.706 10.2 Calculus with Parametric Curves Exercises p.717 10.3 Polar Coordinates Exercises p.730 10.4 Calculus in Polar Coordinates Exercises p.737 10.5 Conic Sections Exercises p.746 10.6 Conic Sections in Polar Coordinates Exercises p.755 Concept Check p.757 True-False Quiz p.757 Review Exercises p.758 Problems p.760

### Chapter 11

Sequences, Series, And Power Series

 11.1 Sequences Exercises p.773 11.2 Series Exercises p.785 11.3 The Integral Test and Estimates of Sums Exercises p.796 11.4 The Comparison Tests Exercises p.802 11.5 Alternating Series and Absolute Convergence Exercises p.810 11.6 The Ratio and Root Tests Exercises p.816 11.7 Strategy for Testing Series Exercises p.819 11.8 Power Series Exercises p.824 11.9 Representations of Functions as Power Series Exercises p.831 11.10 Taylor and Maclaurin Series Exercises p.846 11.11 Application of Taylor Polynomials Exercises p.856 Concept Check p.859 True-False Quiz p.860 Review Exercises p.860 Problems p.863

### Chapter 12

Vectors And The Geometry Of Space

 12.1 Three-Dimensional Coordinate Systems Exercises p.873 12.2 Vectors Exercises p.881 12.3 The Dot Product Exercises p.890 12.4 The Cross Product Exercises p.899 12.5 Equations of Lines and Planes Exercises p.910 12.6 Cylinders and Quadric Surfaces Exercises p.919 Concept Check p.921 True-False Quiz p.922 Review Exercises p.922 Problems p.925

### Chapter 13

Vector Functions

 13.1 Vector Functions and Space Curves Exercises p.933 13.2 Derivatives and Integrals of Vector Functions Exercises p.940 13.3 Arc Length and Curvature Exercises p.951 13.4 Motion in Space: Velocity and Acceleration Exercises p.961 Concept Check p.965 True-False Quiz p.965 Review Exercises p.966 Problems p.968

### Chapter 14

Partial Derivatives

 14.1 Functions of Several Variables Exercises p.984 14.2 Limits and Continuity Exercises p.998 14.3 Partial Derivatives Exercises p.1007 14.4 Tangent Planes and Linear Approximations Exercises p.1019 14.5 The Chain Rule Exercises p.1029 14.6 Directional Derivatives and the Gradient Vector Exercises p.1043 14.7 Maximum and Minimum Values Exercises p.1054 14.8 Lagrange Multipliers Exercises p.1064 Concept Check p.1069 True-False Quiz p.1069 Review Exercises p.1070 Problems p.1073

### Chapter 15

Multiple Integrals

 15.1 Double Integrals Over Rectangles Exercises p.1087 15.2 Double Integrals over General Regions Exercises p.1097 15.3 Double Integrals in Polar Coordinates Exercises p.1105 15.4 Applications of Double Integrals Exercises p.1116 15.5 Surface Area Exercises p.1119 15.6 Triple Integrals Exercises p.1130 15.7 Triple Integrals in Cylindrical Coordinates Exercises p.1138 15.8 Triple Integrals in Spherical Coordinates Exercises p.1144 15.9 Change of Variables in Multiple Integrals Exercises p.1154 Concept Check p.1155 True-False Quiz p.1156 Review Exercises p.1156 Problems p.1159

### Chapter 16

Vector Calculus

 16.1 Vector Fields Exercises p.1167 16.2 Line Integrals Exercises p.1179 16.3 The Fundamental Theorem for Line Integrals Exercises p.1189 16.4 Green's Theorem Exercises p.1197 16.5 Curl and Divergence Exercises p.1206 16.6 Parametric Surfaces and Their Areas Exercises p.1218 16.7 Surface Integrals Exercises p.1230 16.8 Stoke's Theorem Exercises p.1237 16.9 The Divergence Theorem Exercises p.1244 Concept Check p.1247 True-False Quiz p.1247 Review Exercises p.1248 Problems p.1251
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