Calculus, 11th Edition

Calculus, 11th Edition Calculus, 11th Edition

ISBN: 9781337275347 / 1337275344

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Table of Contents

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
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