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Calculus: Early Transcendentals

Calculus: Early Transcendentals, 8th Edition

Calculus: Early Transcendentals, 8th Edition

Calculus: Early Transcendentals, 8th Edition

ISBN: 9781305482463 / 1305482468


Table of Contents

Chapter 1

Functions And Models

1.1Four Ways to Represent a FunctionExercisesp.19
1.2Mathematical Models: A Catalog of Essential FunctionsExercisesp.33
1.3New Functions from Old FunctionsExercisesp.42
1.4Exponential FunctionsExercisesp.53
1.5Inverse Functions and LogarithmsExercisesp.66
Review: Concept Checkp.68
Review: Exercisesp.69
Review: True-False Quizp.69
Problems Plusp.76

Chapter 2

Limits And Derivatives

2.1The Tangent and Velocity ProblemsExercisesp.82
2.2The Limit of a FunctionExercisesp.92
2.3Calculating Limits Using the Limit LawsExercisesp.102
2.4The Precise Definition of a LimitExercisesp.113
2.5ContinuityExercisesp.124
2.6Limits at Infinity; Horizontal AsymptotesExercisesp.137
2.7Derivatives and Rates of ChangeExercisesp.148
2.8The Derivative as a FunctionExercisesp.160
Review: Concept Checkp.165
Review: True-False Quizp.166
Review: Exercisesp.166
Problems Plusp.169

Chapter 3

Differentiation Rules

3.1Derivatives of Polynomials and Exponential FunctionsExercisesp.180
3.2The Product and Quotient RulesExercisesp.188
3.3Derivatives of Trigonometric FunctionsExercisesp.196
3.4The Chain RuleExercisesp.204
3.5Implicit DifferentiationExercisesp.215
3.6Derivatives of Logarithmic FunctionsExercisesp.223
3.7Rates of Change in the Natural and Social SciencesExercisesp.233
3.8Exponential Growth and DecayExercisesp.242
3.9Related RatesExercisesp.249
3.10Linear Approximations and DifferentialsExercisesp.256
3.11Hyperbolic FunctionsExercisesp.264
Review: Concept Checkp.266
Review: True-False Quizp.266
Review: Concept Checkp.267
Problems Plusp.271

Chapter 4

Applications Of Differentiation

4.1Maximum and Minimum ValuesExercisesp.283
4.2The Mean Value TheoremExercisesp.291
4.3How Derivatives Affect the Shape of a GraphExercisesp.300
4.4Indeterminate Forms and l’Hospital’s RuleExercisesp.311
4.5Summary of Curve SketchingExercisesp.321
4.6Graphing with Calculus and CalculatorsExercisesp.329
4.7Optimization ProblemsExercisesp.336
4.8Newton’s MethodExercisesp.348
4.9AntiderivativesExercisesp.355
Review: True-False Quizp.358
Review: Concept Checkp.358
Review: Exercisesp.359
Problems Plusp.363

Chapter 5

Integrals

5.1Areas and DistancesExercisesp.375
5.2The Definite IntegralExercisesp.388
5.3The Fundamental Theorem of CalculusExercisesp.399
5.4Indefinite Integrals and the Net Change TheoremExercisesp.408
5.5The Substitution RuleExercisesp.418
Review: Concept Checkp.421
Review: True-False Quizp.421
Review: Exercisesp.422
Problems Plusp.425

Chapter 6

Applications Of Integration

6.1Areas Between CurvesExercisesp.434
6.2VolumesExercisesp.446
6.3Volumes by Cylindrical ShellsExercisesp.453
6.4WorkExercisesp.458
6.5Average Value of a FunctionExercisesp.463
Review: Concept Checkp.466
Review: Exercisesp.466
Problems Plusp.468

Chapter 7

Techniques Of Integration

7.1Integration by PartsExercisesp.476
7.2Trigonometric IntegralsExercisesp.484
7.3Trigonometric SubstitutionExercisesp.491
7.4Integration of Rational Functions by Partial FractionsExercisesp.501
7.5Strategy for IntegrationExercisesp.507
7.6Integration Using Tables and Computer Algebra SystemsExercisesp.512
7.7Approximate IntegrationExercisesp.524
7.8Improper IntegralsExercisesp.534
Review: True-False Quizp.537
Review: Exercisesp.537
Review: Concept Checkp.537
Problems Plusp.541

Chapter 8

Further Applications Of Integration

8.1Arc LengthExercisesp.548
8.2Area of a Surface of RevolutionExercisesp.555
8.3Applications to Physics and EngineeringExercisesp.565
8.4Applications to Economics and BiologyExercisesp.572
8.5ProbabilityExercisesp.579
Review: Exercisesp.581
Review: Concept Checkp.581
Problems Plusp.583

Chapter 9

Differential Equations

9.1Modeling with Differential EquationsExercisesp.590
9.2Direction Fields and Euler’s MethodExercisesp.597
9.3Separable EquationsExercisesp.605
9.4Models for Population GrowthExercisesp.617
9.5Linear EquationsExercisesp.625
9.6Predator-Prey SystemsExercisesp.631
Review: Exercisesp.634
Review: True-False Quizp.634
Review: Concept Checkp.634
Problems Plusp.637

Chapter 10

Parametric Equations And Polar Coordinates

10.1Curves Defined by Parametric EquationsExercisesp.645
10.2Calculus with Parametric CurvesExercisesp.655
10.3Polar CoordinatesExercisesp.666
10.4Areas and Lengths in Polar CoordinatesExercisesp.672
10.5Conic SectionsExercisesp.680
10.6Conic Sections in Polar CoordinatesExercisesp.688
Review: True-False Quizp.689
Review: Concept Checkp.689
Review: Exercisesp.690
Problems Plusp.692

Chapter 11

Infinite Sequences And Series

11.1SequencesExercisesp.704
11.2SeriesExercisesp.715
11.3The Integral Test and Estimates of SumsExercisesp.725
11.4The Comparison TestsExercisesp.731
11.5Alternating SeriesExercisesp.736
11.6Absolute Convergence and the Ratio and Root TestsExercisesp.742
11.7Strategy for Testing SeriesExercisesp.746
11.8Power SeriesExercisesp.751
11.9Representations of Functions as Power SeriesExercisesp.757
11.10Taylor and Maclaurin SeriesExercisesp.771
11.11Applications of Taylor PolynomialsExercisesp.780
Review: Concept Checkp.784
Review: True-False Quizp.784
Review: Exercisesp.785
Problems Plusp.787

Chapter 12

Vectors And The Geometry Of Space

12.1Three-Dimensional Coordinate SystemsExercisesp.796
12.2VectorsExercisesp.805
12.3The Dot ProductExercisesp.812
12.4The Cross ProductExercisesp.821
12.5Equations of Lines and PlanesExercisesp.831
12.6Cylinders and Quadric SurfacesExercisesp.839
Review: Concept Checkp.841
Review: True-False Quizp.842
Review: Exercisesp.842
Problems Plusp.844

Chapter 13

Vector Functions

13.1Vector Functions and Space CurvesExercisesp.853
13.2Derivatives and Integrals of Vector FunctionsExercisesp.860
13.3Arc Length and CurvatureExercisesp.868
13.4Motion in Space: Velocity and AccelerationExercisesp.878
Review: Concept Checkp.881
Review: True-False Quizp.881
Review: Exercisesp.882
Problems Plusp.884

Chapter 14

Partial Derivatives

14.1Functions of Several VariablesExercisesp.899
14.2Limits and ContinuityExercisesp.910
14.3Partial DerivativesExercisesp.923
14.4Tangent Planes and Linear ApproximationsExercisesp.934
14.5The Chain RuleExercisesp.943
14.6Directional Derivatives and the Gradient VectorExercisesp.956
14.7Maximum and Minimum ValuesExercisesp.967
14.8Lagrange MultipliersExercisesp.977
Review: Concept Checkp.981
Review: True-False Quizp.982
Review: Exercisesp.982
Problems Plusp.985

Chapter 15

Multiple Integrals

15.1Double Integrals over RectanglesExercisesp.999
15.2Double Integrals over General RegionsExercisesp.1008
15.3Double Integrals in Polar CoordinatesExercisesp.1014
15.4Applications of Double IntegralsExercisesp.1024
15.5Surface AreaExercisesp.1028
15.6Triple IntegralsExercisesp.1037
15.7Triple Integrals in Cylindrical CoordinatesExercisesp.1043
15.8Triple Integrals in Spherical CoordinatesExercisesp.1049
15.9Change of Variables in Multiple IntegralsExercisesp.1060
Review: Concept Checkp.1061
Review: True-False Quizp.1061
Review: Exercisesp.1062

Chapter 16

Vector Calculus

Problems Plusp.1065
16.1Vector FieldsExercisesp.1073
16.2Line IntegralsExercisesp.1084
16.3The Fundamental Theorem for Line IntegralsExercisesp.1094
16.4Green’s TheoremExercisesp.1101
16.5Curl and DivergenceExercisesp.1109
16.6Parametric Surfaces and Their AreasExercisesp.1120
16.7Surface IntegralsExercisesp.1132
16.8Stoke’s TheoremExercisesp.1139
16.9The Divergence TheoremExercisep.1145
Review: True-False Quizp.1148
Review: Concept Checkp.1148
Review: Exercisesp.1149
Problems Plusp.1151

Chapter 17

Second-Order Differential Equations

17.1Second-Order Linear EquationsExercisesp.1160
17.2Nonhomogeneous Linear EquationsExercisesp.1167
17.3Applications of Second-Order Differential EquationsExercisesp.1175
17.4Series SolutionsExercisesp.1180
Review: True-False Quizp.1181
Review: Concept Checkp.1181
Review: Exercisesp.1181
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