Calculus, 8th Edition Calculus, 8th Edition

Calculus, 8th Edition

8th Edition | ISBN: 9781305480513 / 1305480511

8,255

expert-verified solutions in this book

Calculus, 8th Edition
Buy on Amazon.com

8th Edition | ISBN: 9781305480513 / 1305480511

8,255

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.19
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.49
1.5 The Limit of a Function Exercises p.59
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.91
Concept Check p.94
True-False Quiz p.95
Review Exercises p.96
Problem Solving p.102

Chapter 2

Derivatives

2.1 Derivatives and Rates of Change Exercises p.113
2.2 The Derivative as a Function Exercises p.125
2.3 Differentiation Formulas Exercises p.140
2.4 Derivatives of Trigonometric Functions Exercises p.150
2.5 The Chain Rule Exercises p.158
2.6 Implicit Differentiation Exercises p.166
2.7 Rates of Change in the Natural and Social Sciences Exercises p.178
2.8 Related Rates Exercises p.185
2.9 Linear Aproximations and Differentials Exercises p.192
Concept Check p.195
True-False Quiz p.196
Review Exercises p.196
Problems Plus p.200

Chapter 3

Applications Of Differentiation

3.1 Maximum and Minimum Values Exercises p.211
3.2 The Mean Value Theorem Exercises p.219
3.3 How Derivatives Affect the Shape of a Graph Exercises p.227
3.4 Limits at Infinity; Horizontal Asymptotes Exercises p.241
3.5 Summary of Curve Sketching Exercises p.250
3.6 Graphing with Calculus and Calculators Exercises p.257
3.7 Optimization Problems Exercises p.264
3.8 Newton's Method Exercises p.276
3.9 Antiderivatives Exercises p.282
Concept Check p.285
True-False Quiz p.285
Review Exercises p.286
Problems Plus p.290

Chapter 4

Integrals

4.1 Areas and Distances Exercises p.303
4.2 The Definite Integral Exercises p.316
4.3 The Fundamental Theorem of Calculus Exercises p.327
4.4 Indefinite Integrals and the Net Change Theorem Exercises p.336
4.5 The Substitution Rule Exercises p.346
Concept Check p.348
True-False Quiz p.348
Review Exercises p.349
Problems Plus p.353

Chapter 5

Applications Of Integration

5.1 Areas Between Curves Exercises p.362
5.2 Volumes Exercises p.374
5.3 Volumes by Cylindrical Shells Exercises p.381
5.4 Work Exercises p.386
5.5 Average Value of a Function Exercises p.391
Concept Check p.393
Review Exercises p.393
Problems Plus p.395

Chapter 6

Inverse Functions

6.1 Inverse Functions Exercises p.406
6.2 Exponential Functions and Their Derivatives Exercises p.418
6.3 Logarithmic Functions Exercises p.426
6.4 Derivatives of Logarithmic Functions Exercises p.436
6.2* The Natural Logarithmic Function Exercises p.445
6.3* The Natural Exponential Function Exercises p.452
6.4* General Logarithmic and Exponential Functions Exercises p.463
6.5 Exponential Growth and Decay Exercises p.471
6.6 Inverse Trigonometric Functions Exercises p.481
6.7 Hyperbolic Functions Exercises p.489
6.8 Indeterminate Forms and l'Hospital's Rule Exercises p.499
Concept Check p.503
True-False Quiz p.504
Review Exercises p.505
Problems Plus p.509

Chapter 7

Techniques Of Integration

7.1 Integration by Parts Exercises p.516
7.2 Trigonometric Integrals Exercises p.524
7.3 Trigonometric Substitution Exercises p.531
7.4 Integration of Rational Functions by Partial Fractions Exercises p.541
7.5 Strategy for Integration Exercises p.547
7.6 Integration Using Tables and Computer Algebra Systems Exercises p.552
7.7 Approximate Integration Exercises p.564
7.8 Improper Integrals Exercises p.574
Review: Concept Check p.577
Review: True-False Quiz p.577
Review: Exercises p.577
Problems Plus p.581

Chapter 8

Further Applications Of Integration

8.1 Arc Length Exercises p.588
8.2 Area of a Surface of Revolution Exercises p.595
8.3 Applications to Physics and Engineering Exercises p.605
8.4 Applications to Economics and Biology Exercises p.612
8.5 Probability Exercises p.619
Review: Concept Check p.621
Review: Exercises p.621
Problems Plus p.623

Chapter 9

Differential Equations

9.1 Modeling with Differential Equations Exercises p.630
9.2 Direction Fields and Euler's Method Exercises p.637
9.3 Separable Equations Exercises p.645
9.4 Models for Population Growth Exercises p.657
9.5 Linear Equations Exercises p.665
9.6 Predator-Prey Systems Exercises p.671
Review: Concept Check p.674
Review: True-False Quiz p.674
Review: Exercises p.674
Problems Plus p.677

Chapter 10

Parametric Equations And Polar Coordinates

10.1 Curves Defined by Parametric Equations Exercises p.685
10.2 Calculus with Parametric Curves Exercises p.695
10.3 Polar Coordinates Exercises p.706
10.4 Areas and Lengths in Polar Coordinates Exercises p.712
10.5 Conic Sections Exercises p.720
10.6 Conic Sections in Polar Coordinates Exercises p.728
Review: Concept Check p.729
Review: True-False Quiz p.729
Review: Exercises p.730
Problems Plus p.732

Chapter 11

Infinite Sequences And Series

11.1 Sequences Exercises p.744
11.2 Series Exercises p.755
11.3 The Integral Test and Estimates of Sums Exercises p.765
11.4 The Comparison Tests Exercises p.771
11.5 Alternating Series Exercises p.776
11.6 Absolute Convergence and the Ratio and Root Tests Exercises p.782
11.7 Strategy for Testing Series Exercises p.786
11.8 Power Series Exercises p.791
11.9 Representations of Functions as Power Series Exercises p.797
11.10 Taylor and Maclaurin Series Exercises p.811
11.11 Applications of Taylor Polynomials Exercises p.820
Review: Concept Check p.824
Review: True-False Quiz p.824
Review: Exercises p.825
Problems Plus p.827

Chapter 12

Vectors And The Geometry Of Space

12.1 Three-Dimensional Coordinate Systems Exercises p.836
12.2 Vectors Exercises p.845
12.3 The Dot Product Exercises p.852
12.4 The Cross Product Exercises p.861
12.5 Equations of Lines and Planes Exercises p.871
12.6 Cylinders and Quadric Surfaces Exercises p.879
Review: Concept Check p.881
Review: True-False Quiz p.882
Review: Exercises p.882
Problems Plus p.884

Chapter 13

Vector Functions

13.1 Vector Functions and Space Curves Exercises p.893
13.2 Derivatives and Integrals of Vector Functions Exercises p.900
13.3 Arc Length and Curvature Exercises p.908
13.4 Motion in Space: Velocity and Acceleration Exercises p.918
Review: Concept Check p.921
Review: True-False Quiz p.921
Review: Exercises p.922
Problems Plus p.924

Chapter 14

Partial Derivatives

14.1 Functions of Several Variables Exercises p.939
14.2 Limits and Continuity Exercises p.950
14.3 Partial Derivatives Exercises p.963
14.4 Tangent Planes and Linear Approximations Exercises p.974
14.5 The Chain Rule Exercises p.983
14.6 Directional Derivatives and the Gradient Vector Exercises p.996
14.7 Maximum and Minimum Values Exercises p.1007
14.8 Lagrange Multipliers Exercises p.1017
Review: Concept Check p.1021
Review: True-False Quiz p.1022
Review: Exercises p.1022
Problems Plus p.1025

Chapter 15

Multiple Integrals

15.1 Double Integrals over Rectangles Exercises p.1039
15.2 Double Integrals over General Regions Exercises p.1048
15.3 Double Integrals in Polar Coordinates Exercises p.1054
15.4 Applications of Double Integrals Exercises p.1064
15.5 Surface Area Exercises p.1068
15.6 Triple Integrals Exercises p.1077
15.7 Triple Integrals in Cylindrical Coordinates Exercises p.1083
15.8 Triple Integrals in Spherical Coordinates Exercises p.1089
15.9 Change of Variables in Multiple Integrals Exercises p.1100
Review: Concept Check p.1101
Review: True-False Quiz p.1101
Review: Exercises p.1102
Problems Plus p.1105

Chapter 16

Vector Calculus

16.1 Vector Fields Exercises p.1113
16.2 Line Integrals Exercises p.1124
16.3 The Fundamental Theorem for Line Integrals Exercises p.1134
16.4 Green's Theorem Exercises p.1141
16.5 Curl and Divergence Exercises p.1149
16.6 Parametric Surfaces and Their Areas Exercises p.1160
16.7 Surface Integrals Exercises p.1172
16.8 Stoke's Theorem Exercises p.1179
16.9 The Divergence Theorem Exercise p.1185
Review: Concept Check p.1188
Review: True-False Quiz p.1188
Review: Exercises p.1189
Problems Plus p.1191

Chapter 17

Second-Order Differential Equations

17.1 Second-Order Linear Equations Exercises p.1200
17.2 Nonhomogeneous Linear Equations Exercises p.1207
17.3 Applications of Second-Order Differential Equations Exercises p.1215
17.4 Series Solutions Exercises p.1220
Review: Concept Check p.1221
Review: True-False Quiz p.1221
Review: Exercises p.1221
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