Calculus: Early Transcendentals, 8th Edition Calculus: Early Transcendentals, 8th Edition

Calculus: Early Transcendentals, 8th Edition

8th Edition | ISBN: 9781305482463 / 1305482468


expert-verified solutions in this book

Calculus: Early Transcendentals, 8th Edition
Buy on

8th Edition | ISBN: 9781305482463 / 1305482468


expert-verified solutions in this book

Buy on

Table of Contents

Chapter 1

Functions And Models

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 Exponential Functions Exercises p.53
1.5 Inverse Functions and Logarithms Exercises p.66
Review: Concept Check p.68
Review: True-False Quiz p.69
Review: Exercises p.69
Problems Plus p.76

Chapter 2

Limits And Derivatives

2.1 The Tangent and Velocity Problems Exercises p.82
2.2 The Limit of a Function Exercises p.92
2.3 Calculating Limits Using the Limit Laws Exercises p.102
2.4 The Precise Definition of a Limit Exercises p.113
2.5 Continuity Exercises p.124
2.6 Limits at Infinity; Horizontal Asymptotes Exercises p.137
2.7 Derivatives and Rates of Change Exercises p.148
2.8 The Derivative as a Function Exercises p.160
Review: Concept Check p.165
Review: True-False Quiz p.166
Review: Exercises p.166
Problems Plus p.169

Chapter 3

Differentiation Rules

3.1 Derivatives of Polynomials and Exponential Functions Exercises p.180
3.2 The Product and Quotient Rules Exercises p.188
3.3 Derivatives of Trigonometric Functions Exercises p.196
3.4 The Chain Rule Exercises p.204
3.5 Implicit Differentiation Exercises p.215
3.6 Derivatives of Logarithmic Functions Exercises p.223
3.7 Rates of Change in the Natural and Social Sciences Exercises p.233
3.8 Exponential Growth and Decay Exercises p.242
3.9 Related Rates Exercises p.249
3.10 Linear Approximations and Differentials Exercises p.256
3.11 Hyperbolic Functions Exercises p.264
Review: Concept Check p.266
Review: True-False Quiz p.266
Review: Concept Check p.267
Problems Plus p.271

Chapter 4

Applications Of Differentiation

4.1 Maximum and Minimum Values Exercises p.283
4.2 The Mean Value Theorem Exercises p.291
4.3 How Derivatives Affect the Shape of a Graph Exercises p.300
4.4 Indeterminate Forms and l'Hospital's Rule Exercises p.311
4.5 Summary of Curve Sketching Exercises p.321
4.6 Graphing with Calculus and Calculators Exercises p.329
4.7 Optimization Problems Exercises p.336
4.8 Newton's Method Exercises p.348
4.9 Antiderivatives Exercises p.355
Review: Concept Check p.358
Review: True-False Quiz p.358
Review: Exercises p.359
Problems Plus p.363

Chapter 5


5.1 Areas and Distances Exercises p.375
5.2 The Definite Integral Exercises p.388
5.3 The Fundamental Theorem of Calculus Exercises p.399
5.4 Indefinite Integrals and the Net Change Theorem Exercises p.408
5.5 The Substitution Rule Exercises p.418
Review: Concept Check p.421
Review: True-False Quiz p.421
Review: Exercises p.422
Problems Plus p.425

Chapter 6

Applications Of Integration

6.1 Areas Between Curves Exercises p.434
6.2 Volumes Exercises p.446
6.3 Volumes by Cylindrical Shells Exercises p.453
6.4 Work Exercises p.458
6.5 Average Value of a Function Exercises p.463
Review: Concept Check p.466
Review: Exercises p.466
Problems Plus p.468

Chapter 7

Techniques Of Integration

7.1 Integration by Parts Exercises p.476
7.2 Trigonometric Integrals Exercises p.484
7.3 Trigonometric Substitution Exercises p.491
7.4 Integration of Rational Functions by Partial Fractions Exercises p.501
7.5 Strategy for Integration Exercises p.507
7.6 Integration Using Tables and Computer Algebra Systems Exercises p.512
7.7 Approximate Integration Exercises p.524
7.8 Improper Integrals Exercises p.534
Review: True-False Quiz p.537
Review: Concept Check p.537
Review: Exercises p.537
Problems Plus p.541

Chapter 8

Further Applications Of Integration

8.1 Arc Length Exercises p.548
8.2 Area of a Surface of Revolution Exercises p.555
8.3 Applications to Physics and Engineering Exercises p.565
8.4 Applications to Economics and Biology Exercises p.572
8.5 Probability Exercises p.579
Review: Concept Check p.581
Review: Exercises p.581
Problems Plus p.583

Chapter 9

Differential Equations

9.1 Modeling with Differential Equations Exercises p.590
9.2 Direction Fields and Euler's Method Exercises p.597
9.3 Separable Equations Exercises p.605
9.4 Models for Population Growth Exercises p.617
9.5 Linear Equations Exercises p.625
9.6 Predator-Prey Systems Exercises p.631
Review: Concept Check p.634
Review: True-False Quiz p.634
Review: Exercises p.634
Problems Plus p.637

Chapter 10

Parametric Equations And Polar Coordinates

10.1 Curves Defined by Parametric Equations Exercises p.645
10.2 Calculus with Parametric Curves Exercises p.655
10.3 Polar Coordinates Exercises p.666
10.4 Areas and Lengths in Polar Coordinates Exercises p.672
10.5 Conic Sections Exercises p.680
10.6 Conic Sections in Polar Coordinates Exercises p.688
Review: True-False Quiz p.689
Review: Concept Check p.689
Review: Exercises p.690
Problems Plus p.692

Chapter 11

Infinite Sequences And Series

11.1 Sequences Exercises p.704
11.2 Series Exercises p.715
11.3 The Integral Test and Estimates of Sums Exercises p.725
11.4 The Comparison Tests Exercises p.731
11.5 Alternating Series Exercises p.736
11.6 Absolute Convergence and the Ratio and Root Tests Exercises p.742
11.7 Strategy for Testing Series Exercises p.746
11.8 Power Series Exercises p.751
11.9 Representations of Functions as Power Series Exercises p.757
11.10 Taylor and Maclaurin Series Exercises p.771
11.11 Applications of Taylor Polynomials Exercises p.780
Review: Concept Check p.784
Review: True-False Quiz p.784
Review: Exercises p.785
Problems Plus p.787

Chapter 12

Vectors And The Geometry Of Space

12.1 Three-Dimensional Coordinate Systems Exercises p.796
12.2 Vectors Exercises p.805
12.3 The Dot Product Exercises p.812
12.4 The Cross Product Exercises p.821
12.5 Equations of Lines and Planes Exercises p.831
12.6 Cylinders and Quadric Surfaces Exercises p.839
Review: Concept Check p.841
Review: True-False Quiz p.842
Review: Exercises p.842
Problems Plus p.844

Chapter 13

Vector Functions

13.1 Vector Functions and Space Curves Exercises p.853
13.2 Derivatives and Integrals of Vector Functions Exercises p.860
13.3 Arc Length and Curvature Exercises p.868
13.4 Motion in Space: Velocity and Acceleration Exercises p.878
Review: True-False Quiz p.881
Review: Concept Check p.881
Review: Exercises p.882
Problems Plus p.884

Chapter 14

Partial Derivatives

14.1 Functions of Several Variables Exercises p.899
14.2 Limits and Continuity Exercises p.910
14.3 Partial Derivatives Exercises p.923
14.4 Tangent Planes and Linear Approximations Exercises p.934
14.5 The Chain Rule Exercises p.943
14.6 Directional Derivatives and the Gradient Vector Exercises p.956
14.7 Maximum and Minimum Values Exercises p.967
14.8 Lagrange Multipliers Exercises p.977
Review: Concept Check p.981
Review: True-False Quiz p.982
Review: Exercises p.982
Problems Plus p.985

Chapter 15

Multiple Integrals

15.1 Double Integrals over Rectangles Exercises p.999
15.2 Double Integrals over General Regions Exercises p.1008
15.3 Double Integrals in Polar Coordinates Exercises p.1014
15.4 Applications of Double Integrals Exercises p.1024
15.5 Surface Area Exercises p.1028
15.6 Triple Integrals Exercises p.1037
15.7 Triple Integrals in Cylindrical Coordinates Exercises p.1043
15.8 Triple Integrals in Spherical Coordinates Exercises p.1049
15.9 Change of Variables in Multiple Integrals Exercises p.1060
Review: Concept Check p.1061
Review: True-False Quiz p.1061
Review: Exercises p.1062

Chapter 16

Vector Calculus

Problems Plus p.1065
16.1 Vector Fields Exercises p.1073
16.2 Line Integrals Exercises p.1084
16.3 The Fundamental Theorem for Line Integrals Exercises p.1094
16.4 Green's Theorem Exercises p.1101
16.5 Curl and Divergence Exercises p.1109
16.6 Parametric Surfaces and Their Areas Exercises p.1120
16.7 Surface Integrals Exercises p.1132
16.8 Stoke's Theorem Exercises p.1139
16.9 The Divergence Theorem Exercise p.1145
Review: Concept Check p.1148
Review: True-False Quiz p.1148
Review: Exercises p.1149
Problems Plus p.1151

Chapter 17

Second-Order Differential Equations

17.1 Second-Order Linear Equations Exercises p.1160
17.2 Nonhomogeneous Linear Equations Exercises p.1167
17.3 Applications of Second-Order Differential Equations Exercises p.1175
17.4 Series Solutions Exercises p.1180
Review: True-False Quiz p.1181
Review: Concept Check p.1181
Review: Exercises p.1181
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