Calculus Of A Single Variable, 9th Edition

Calculus Of A Single Variable, 9th Edition Calculus Of A Single Variable, 9th Edition

ISBN: 9781111785444 / 1111785449

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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

Chapter 1

Limits And Their Properties

1.1 A Preview of Calculus Exercises p.47
1.2 Finding Limits Graphically and Numerically Exercises p.54
1.3 Evaluating Limits Analytically Exercises p.67
1.4 Continuity and One-Sided Limits Exercises p.78
1.5 Infinite Limits Exercises p.88
Review Exercises p.91
Problem Solving p.93
AB/BC Test Prep Questions p.AP1-2

Chapter 2

Differentiation

AB/BC Test Prep Questions p.AP2-1
2.1 The Derivative and the Tangent Line Problem Exercises p.103
2.2 Basic Differentiation Rules and Rates of Change Exercises p.115
2.3 Product and Quotient Rules and Higher-Order Derivatives Exercises p.126
2.4 The Chain Rule Exercises p.137
2.5 Implicit Differentiation Exercises p.146
2.6 Related Rates Exercises p.154
Review Exercises p.158
Problem Solving p.161

Chapter 3

Applications Of Differentiation

AB/BC Test Prep Questions p.AP3-2
3.1 Extrema on an Interval Exercises p.169
3.2 Rolle's Theorem and the Mean Value Theorem Exercises p.176
3.3 Increasing and Decreasing Functions and the First Derivative Test Exercises p.186
3.4 Concavity and the Second Derivative Test Exercises p.195
3.5 Limits at Infinity Exercises p.205
3.6 A Summary of Curve Sketching Exercises p.215
3.7 Optimization Problems Exercises p.223
3.8 Newton's Method Exercises p.233
3.9 Differentials Exercises p.240
Review Exercises p.242
Problem Solving p.245

Chapter 4

Integration

AB/BC Test Prep Questions p.AP4-2
4.1 Antiderivatives and Indefinite Integration Exercises p.255
4.2 Area Exercises p.267
4.3 Riemann Sums and Definite Integrals Exercises p.278
4.4 The Fundamental Theorem of Calculus Exercises p.293
4.5 Integration by Substitution Exercises p.306
4.6 Numerical Integration Exercises p.316
Review Exercises p.318
Problem Solving p.321

Chapter 5

Logarithmic, Exponential, And Other Transcendental Functions

AB/BC Test Prep Questions p.AP5-1
5.1 The Natural Logarithmic Function: Differentiation Exercises p.331
5.2 The Natural Logarithmic Function: Integration Exercises p.340
5.3 Inverse Functions Exercises p.349
5.4 Exponential Functions: Differentiation and Integration Exercises p.358
5.5 Bases Other Than "e" and Applications Exercises p.368
5.6 Inverse Trigonometric Functions: Differentiation Exercises p.379
5.7 Inverse Trigonometric Functions: Integration Exercises p.387
5.8 Hyperbolic Functions Exercises p.398
Review Exercises p.401
Problem Solving p.403

Chapter 6

Differential Equations

AB/BC Test Prep Questions p.AP6-1
6.1 Slope Fields and Euler's Method Exercises p.411
6.2 Differential Equations: Growth and Decay Exercises p.420
6.3 Separation of Variables and the Logistic Equation Exercises p.431
6.4 First-Order Linear Differential Equations Exercises p.440
Review Exercises p.443
Problem Solving p.445

Chapter 7

Applications Of Integration

AB/BC Test Prep Questions p.AP7-1
7.1 Area of a Region Between Two Curves Exercises p.454
7.2 Volume: The Disk Method Exercises p.465
7.3 Volume: The Shell Method Exercises p.474
7.4 Arc Length and Surfaces of Revolution Exercises p.485
7.5 Work Exercises p.495
7.6 Moments, Centers of Mass, and Centroids Exercises p.506
7.7 Fluid Pressure and Fluid Force Exercises p.513
Review Exercises p.515
Problem Solving p.517

Chapter 8

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

AB/BC Test Prep Questions p.AP8-1
8.1 Basic Integration Rules Exercises p.524
8.2 Integration by Parts Exercises p.533
8.3 Trigonometric Integrals Exercises p.542
8.4 Trigonometric Substitution Exercises p.551
8.5 Partial Fractions Exercises p.561
8.6 Integration by Tables and Other Integration Techniques Exercises p.567
8.7 Indeterminate Forms and L'Hôpital's Rule Exercises p.576
8.8 Improper Integrals Exercises p.587
Review Exercises p.591
Problem Solving p.593

Chapter 9

Infinite Series

AB/BC Test Prep Questions p.AP9-1
9.1 Sequences Exercises p.604
9.2 Series and Convergence Exercises p.614
9.3 The Integral Test and p-Series Exercises p.622
9.4 Comparisons of Series Exercises p.630
9.5 Alternating Series Exercises p.638
9.6 The Ratio and Root Tests Exercises p.647
9.7 Taylor Polynomials and Approximations Exercises p.658
9.8 Power Series Exercises p.668
9.9 Representation of Functions by Power Series Exercises p.676
9.10 Taylor and Maclaurin Series Exercises p.687
Review Exercises p.690
Problem Solving p.693

Chapter 10

Conics, Parametric Equations, And Polar Coordinates

AB/BC Test Prep Questions p.AP10-1
10.1 Conics and Calculus Exercises p.706
10.2 Plane Curves and Parametric Equations Exercises p.718
10.3 Parametric Equations and Calculus Exercises p.727
10.4 Polar Coordinates and Polar Graphs Exercises p.738
10.5 Area and Arc Length in Polar Coordinates Exercises p.747
10.6 Polar Equations of Conics and Kepler's Laws Exercises p.755
Review Exercises p.758
Problem Solving p.761

Chapter 11

Vectors And The Geometry Of Space

AB/BC Test Prep Questions p.AP11-1
11.1 Vectors in the Plane Exercises p.771
11.2 Space Coordinates and Vectors in Space Exercises p.780
11.3 The Dot Product of Two Vectors Exercises p.789
11.4 The Cross Product of Two Vectors in Space Exercises p.798
11.5 Lines and Planes in Space Exercises p.807
11.6 Surfaces in Space Exercises p.820
11.7 Cylindrical And Spherical Coordinates Exercises p.827
Review Exercises p.829
Problem Solving p.831
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