Calculus, 10th Edition

Calculus, 10th Edition Calculus, 10th Edition

ISBN: 9781285057095 / 1285057090

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 Fitting Models to Data Exercises p.34
Review Exercises p.37
Problem Solving p.39

Chapter 1

Limits And Their Properties

1.1 A Preview of Calculus Exercises p.47
1.2 Finding Limits Graphically and Numerically Exercises p.55
1.3 Evaluating Limits Analytically Exercises p.67
1.4 Continuity and One-Sided Limits Exercises p.79
1.5 Infinite Limits Exercises p.88
Review Exercises p.91
Problem Solving p.93

Chapter 2

Differentiation

2.1 The Derivative and the Tangent Line Problem Exercises p.103
2.2 Basic Differentiation Rules and Rates of Change Exercises p.114
2.3 Product and Quotient Rules and Higher-Order Derivatives Exercises p.125
2.4 The Chain Rule Exercises p.136
2.5 Implicit Differentiation Exercises p.145
2.6 Related Rates Exercises p.153
Review Exercises p.157
Problem Solving p.159

Chapter 3

Applications Of Differentiation

3.1 Extrema on an Interval Exercises p.167
3.2 Rolle's Theorem and the Mean Value Theorem Exercises p.174
3.3 Increasing and Decreasing Functions and the First Derivative Test Exercises p.183
3.4 Concavity and the Second Derivative Test Exercises p.192
3.5 Limits at Infinity Exercises p.202
3.6 A Summary of Curve Sketching Exercises p.212
3.7 Optimization Problems Exercises p.220
3.8 Newton's Method Exercises p.229
3.9 Differentials Exercises p.236
Review Exercises p.238
Problem Solving p.241

Chapter 4

Integration

4.1 Antiderivatives and Indefinite Integrals Exercises p.251
4.2 Area Exercises p.263
4.3 Riemann Sums and Definite Integrals Exercises p.273
4.4 The Fundamental Theorem of Calculus Exercises p.288
4.5 Integration by Substitution Exercises p.301
4.6 Numerical Integration Exercises p.310
Review Exercises p.312
Problem Solving p.315

Chapter 5

Logarithmic, Exponential, And Other Transcendental Functions

5.1 The Natural Logarithmic Function: Differentiation Exercises p.325
5.2 The Natural Logarithmic Function: Integration Exercises p.334
5.3 Inverse Functions Exercises p.343
5.4 Exponential Functions: Differentiation and Integration Exercises p.352
5.5 Bases Other than e and Applications Exercises p.362
5.6 Inverse Trigonometric Functions: Differentiation Exercises p.372
5.7 Inverse Trigonometric Functions: Integration Exercises p.380
5.8 Hyperbolic Functions Exercises p.390
Review Exercises p.393
Problem Solving p.395

Chapter 6

Differential Equations

6.1 Slope Fields and Euler's Method Exercises p.403
6.2 Differential Equations: Growth and Decay Exercises p.412
6.3 Separation of Variables and the Logistic Equation Exercises p.421
6.4 First-Order Linear Differential Equations Exercises p.428
Review Exercises p.431
Problem Solving p.433

Chapter 7

Applications Of Integration

7.1 Area of a Region Between Two Curves Exercises p.442
7.2 Volume: The Disk Method Exercises p.453
7.3 Volume: The Shell Method Exercises p.462
7.4 Arc Length and Surfaces of Revolution Exercises p.473
7.5 Work Exercises p.483
7.6 Moments, Centers of Mass, and Centroids Exercises p.494
7.7 Fluid Pressure and Fluid Force Exercises p.501
Review Exercises p.503
Problem Solving p.505

Chapter 8

Integration Techniques, L'Hopital's Rule, And Improper Integrals

8.1 Basic Integration Rules Exercises p.512
8.2 Integration by Parts Exercises p.521
8.3 Trigonometric Integrals Exercises p.530
8.4 Trigonometric Substitution Exercises p.539
8.5 Partial Fractions Exercises p.549
8.6 Integration by Tables and Other Integration Techniques Exercises p.555
8.7 Indeterminate Forms and L'Hopital's Rule Exercises p.564
8.8 Improper Integrals Exercises p.575
Review Exercises p.579
Problem Solving p.581

Chapter 9

Infinite Series

9.1 Sequences Exercises p.592
9.2 Series and Convergence Exercises p.601
9.3 The Integral Test and p-Series Exercises p.609
9.4 Comparisons of Series Exercises p.616
9.5 Alternating Series Exercises p.625
9.6 The Ratio and Root Tests Exercises p.633
9.7 Taylor Polynomials and Approximations Exercises p.644
9.8 Power Series Exercises p.654
9.9 Representation of Functions by Power Series Exercises p.662
9.10 Taylor and Maclaurin Series Exercises p.673
Review Exercises p.676
Problem Solving p.679

Chapter 10

Conics, Parametric Equations, And Polar Coordinates

10.1 Conics and Calculus Exercises p.692
10.2 Plane Curves and Parametric Equations Exercises p.703
10.3 Parametric Equations and Calculus Exercises p.711
10.4 Polar Coordinates and Polar Graphs Exercises p.722
10.5 Area and Arc Length in Polar Coordinates Exercises p.731
10.6 Polar Equations of Conics and Kepler's Laws Exercises p.739
Review Exercises p.742
Problem Solving p.745

Chapter 11

Vectors And The Geometry Of Space

11.1 Vectors in the Plane Exercises p.755
11.2 Space Coordinates and Vectors in Space Exercises p.763
11.3 The Dot Product of Two Vectors Exercises p.773
11.4 The Cross Product of Two Vectors in Space Exercises p.781
11.5 Lines and Planes in Space Exercises p.790
11.6 Surface in Space Exercises p.802
11.7 Cylindrical and Spherical Coordiantes Exercises p.809
Review Exercises p.811
Problem Solving p.813

Chapter 12

Vector-Valued Functions

12.1 Vector-Valued Functions Exercises p.821
12.2 Differentiation and Integration of Vector-Valued Functions Exercises p.830
12.3 Velocity and Acceleration Exercises p.838
12.4 Tangent Vectors and Normal Vectors Exercises p.848
12.5 Arc Length and Curvature Exercises p.860
Review Exercises p.863
Problem Solving p.865

Chapter 13

Functions Of Several Variables

13.1 Introduction to Functions of Several Variables Exercises p.876
13.2 Limits and Continuity Exercises p.887
13.3 Partial Derivatives Exercises p.896
13.4 Differentials Exercises p.905
13.5 Chain Rules for Functions of Several Variables Exercises p.913
13.6 Directional Derivatives and Gradients Exercises p.924
13.7 Tangent Planes and Normal Lines Exercises p.933
13.8 Extrema of Functions of Two Variables Exercises p.942
13.9 Applications of Extrema Exercises p.949
13.10 Lagrange Multipliers Exercises p.958
Review Exercises p.960
Problem Solving p.963

Chapter 14

Multiple Integration

14.1 Iterated Integrals and Area in the Plane Exercises p.972
14.2 Double Integrals and Volume Exercises p.983
14.3 Change of Variables: Polar Coordinates Exercises p.991
14.4 Center of Mass and Moments of Inertia Exercises p.1000
14.5 Surface Area Exercises p.1007
14.6 Triple Integrals and Applications Exercises p.1017
14.7 Triple Integrals in Other Coordinates Exercises p.1025
14.8 Change of Variables: Jacobians Exercises p.1032
Review Exercises p.1034
Problem Solving p.1037

Chapter 15

Vector Analysis

15.1 Vector Fields Exercises p.1049
15.2 Line Integrals Exercises p.1061
15.3 Conservative Vector Fields and Independence of Path Exercises p.1072
15.4 Green's Theorem Exercises p.1081
15.5 Parametric Surfaces Exercises p.1091
15.6 Surface Integrals Exercises p.1104
15.7 Divergence Theorem Exercises p.1112
15.8 Stoke's Theorem Exercises p.1119
Review Exercises p.1120
Problem Solving p.1123
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