# Calculus, 11th Edition Calculus, 11th Edition

11th Edition | ISBN: 9781337275347 / 1337275344

10,578

expert-verified solutions in this book

11th Edition | ISBN: 9781337275347 / 1337275344

10,578

expert-verified solutions in this book

### Chapter P

Preparation For Calculus

 P-1 Graphs and Models Exercises p.8 P-2 Linear Models and Rates of Change Exercises p.16 P-3 Functions and Their Graphs Exercises p.27 P-4 Review of Trigonometric Functions Exercises p.38 Review Exercises p.41 Problem Solving p.43

### Chapter 1

Limits And Their Properties

 1-1 A Preview of Calculus Exercises p.51 1-2 Finding Limits Graphically and Numerically Exercises p.59 1-3 Evaluating Limits Analytically Exercises p.71 1-4 Continuity and One-Sided Limits Exercises p.83 1-5 Infinite Limits Exercises p.92 Review Exercises p.95 Problem Solving p.97

### Chapter 2

Differentiation

 2-1 The Derivative and the Tangent Line Problem Exercises p.107 2-2 Basic Differentiation Rules and Rates of Change Exercises p.118 2-3 Product and Quotient Rules and Higher-Order Derivatives Exercises p.129 2-4 The Chain Rule Exercises p.140 2-5 Implicit Differentiation Exercises p.149 2-6 Related Rates Exercises p.157 Review Exercises p.161 Problem Solving p.163

### Chapter 3

Applications Of Differentiation

 3-1 Extrema on an Interval Exercises p.171 3-2 Rolle's Theorem and the Mean Value Theorem Exercises p.178 3-3 Increasing and Decreasing Functions and the First Derivative Test Exercises p.187 3-4 Concavity and the Second Derivative Test Exercises p.196 3-5 Limits and Infinity Exercises p.206 3-6 A Summary of Curve Sketching Exercises p.215 3-7 Optimization Problems Exercises p.224 3-8 Newton's Method Exercises p.233 3-9 Differentials Exercises p.240 Review Exercises p.242 Problem Solving p.245

### Chapter 4

Integration

 4-1 Antiderivatives and Indefinite Integration Exercises p.255 4-2 Area Exercises p.267 4-3 Riemann Sums and Definite Integrals Exercises p.277 4-4 The Fundamental Theorem of Calculus Exercises p.292 4-5 Integration by Substitution Exercises p.305 Review Exercises p.309 Problem Solving p.311

### Chapter 5

Logarithmic, Exponential, And Other Transcendental Functions

 5-1 The Natural Logarithmic Function: Differentiation Exercises p.321 5-2 The natural Logarithmic Function: Integration Exercises p.330 5-3 Inverse Functions Exercises p.339 5-4 Exponential Functions: Differentiation and Integration Exercises p.348 5-5 Bases Other than e and Applications Exercises p.358 5-6 Indeterminate Forms and L'Hopital's Rule Exercises p.369 5-7 Inverse Trigonometric Functions: Differentiation Exercises p.379 5-8 Inverse Trigonometric Functions: Integration Exercises p.387 5-9 Hyperbolic Functions Exercises p.397 Review Exercises p.400 Problem Solving p.403

### Chapter 6

Differential Equations

 6-1 Slope Fields and Euler's Method Exercises p.411 6-2 Growth and Decay Exercises p.420 6-3 Separation of Variables and the Logistic Equation Exercises p.429 6-4 First-Order Linear Differential Equations Exercises p.436 Review Exercises p.439 Problem Solving p.441

### Chapter 7

Applications Of Integration

 7-1 Area of a Region Between Two Curves Exercises p.450 7-2 Volume: The Disk Method Exercises p.461 7-3 Volume: The Shell Method Exercises p.470 7-4 Arc Length and Surfaces of Revolution Exercises p.481 7-5 Work Exercises p.491 7-6 Moments, Centers of Mass, and Centroids Exercises p.502 7-7 Fluid Pressure and Fluid Force Exercises p.509 Review Exercises p.511 Problem Solving p.513

### Chapter 8

Integration Techniques And Improper Integrals

 8-1 Basic Integration Rules Exercises p.520 8-2 Integration by Parts Exercises p.529 8-3 Trigonometric Integrals Exercises p.538 8-4 Trigonometric Substitution Exercises p.547 8-5 Partial Fractions Exercises p.557 8-6 Numerical Integration Exercises p.564 8-7 Integration by Tables and Other Integration Techniques Exercises p.570 8-8 Improper Integrals Exercises p.579 Review Exercises p.583 Problem Solving p.585

### Chapter 9

Infinite Series

 9-1 Sequences Exercises p.596 9-2 Series and Convergence Exercises p.605 9-3 The Integral Tests and p-Series Exercises p.613 9-4 Comparisons of Series Exercises p.620 9-5 Alternating Series Exercises p.629 9-6 The Ratio and Root Tests Exercises p.637 9-7 Taylor Polynomials and Approximations Exercises p.648 9-8 Power Series Exercises p.658 9-9 Representation of Functions by Power Series Exercises p.666 9-10 Taylor and Maclaurin Series Exercises p.677 Review Exercises p.680 Problem Solving p.683

### Chapter 10

Conics, Parametric Equations, And Polar Coordinates

 10-1 Conics and Calculus Exercises p.696 10-2 Plane Curves and Parametric Equations Exercises p.707 10-3 Parametric Equations and Calculus Exercises p.715 10-4 Polar Coordinates and Polar Graphs Exercises p.726 10-5 Area and Arc Length in Polar Coordinates Exercises p.735 10-6 Polar Equations of Conics and Kepler's Laws Exercises p.743 Review Exercises p.746 Problem Solving p.749

### Chapter 11

Vectors And The Geometry Of Space

 11-1 Vectors in the Plane Exercises p.759 11-2 Space Coordinates and Vectors in Space Exercises p.767 11-3 The Dot Product of Two Vectors Exercises p.777 11-4 The Cross Product of Two Vectors in Space Exercises p.785 11-5 Lines and Planes in Space Exercises p.794 11-6 Surfaces in Space Exercises p.806 11-7 Cylindrical and Spherical Coordinates Exercises p.813 Review Exercises p.815 Problem Solving p.817

### Chapter 12

Vector-Valued Functions

 12-1 Vector-Valued Functions Exercises p.825 12-2 Differentiation and Integration of Vector-Valued Functions Exercises p.834 12-3 Velocity and Acceleration Exercises p.842 12-4 Tangent Vectors and Normal Vectors Exercises p.852 12-5 Arc Length and Curvature Exercises p.864 Review Exercises p.867 Problem Solving p.869

### Chapter 13

Functions Of Several Variables

 13-1 Introduction to Functions of Several Variables Exercises p.880 13-2 Limits and Continuity Exercises p.891 13-3 Partial Derivatives Exercises p.900 13-4 Differentials Exercises p.909 13-5 Chain Rule for Functions of Several Variables Exercises p.917 13-6 Directional Derivatives and Gradients Exercises p.928 13-7 Tangent Planes and Normal Lines Exercises p.937 13-8 Extrema of Functions of Two Variables Exercises p.946 13-9 Applications of Extrema Exercises p.953 13-10 Lagrange Multipliers Exercises p.962 Review Exercises p.964 Problem Solving p.967

### Chapter 14

Multiple Integration

 14-1 Iterated Integrals and Area In the Planes Exercises p.976 14-2 Double Integrals and Volume Exercises p.987 14-3 Change of Variables: Polar Coordinates Exercises p.995 14-4 Center of Mass and Moments of Inertia Exercises p.1004 14-5 Surface Area Exercises p.1011 14-6 Triple Integrals and Applications Exercises p.1021 14-7 Triple Integrals in Other Coordinates Exercises p.1029 14-8 Change of Variables: Jacobians Exercises p.1036 Review Exercises p.1038 Problem Solving p.1041

### Chapter 15

Vector Analysis

 15-1 Vector Fields Exercises p.1053 15-2 Line Integrals Exercises p.1065 15-3 Conservative Vector Fields and Independence of Path Exercises p.1076 15-4 Green's Theorem Exercises p.1085 15-5 Parametric Surfaces Exercises p.1095 15-6 Surface Integrals Exercises p.1108 15-7 Divergence Theorem Exercises p.1116 15-8 Stokes's Theorem Exercises p.1123 Review Exercises p.1124 Problem Solving p.1127