Calculus, 9th Edition Calculus, 9th Edition

Calculus, 9th Edition

9th Edition | ISBN: 9781337624183 / 1337624187

10,688

expert-verified solutions in this book

Calculus, 9th Edition
Buy on Amazon.com

9th Edition | ISBN: 9781337624183 / 1337624187

10,688

expert-verified solutions in this book

Buy on Amazon.com

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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