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Calculus: Graphical, Numerical, Algebraic, 3rd Edition

Calculus: Graphical, Numerical, Algebraic, 3rd Edition Calculus: Graphical, Numerical, Algebraic ...

ISBN: 9780132014083 / 0132014084

Table of Contents

Chapter 1

Prerequisites For Calculus

1.1 Lines Quick review p.9
Exercises p.9
1.2 Functions and Graphs Quick Review p.18
Exercise p.19
1.3 Exponential Functions Quick Review p.26
Exercises p.26
Quick Quiz for AP* Preparation: Sections 1.1 - 1.3 p.29
1.4 Parametric Equations Quick Review p.34
Exercises p.34
1.5 Functions and Logarithms Quick Review p.43
Exercises p.44
1.6 Trigonometric Functions Quick Review 1.6 p.52
Exercises p.52
Quick Quiz for AP* Preparation: Section 1.4-1.6 p.55
Chapter 1 Review Exercises p.56

Chapter 2

Limits And Continuity

2.1 Rates of Change and Limits Quick Review p.65
Exercises p.66
2.2 Limits Involving Infinity Quick Review p.75
Exercises p.76
Quick Quiz for AP* Preparation: Section 2.1 and 2.2 p.77
2.3 Continuity Quick Review p.84
Exercises p.84
2.4 Rates of Change and Tangent Lines Quick Review p.92
Exercises p.92
Quick Quiz for AP* Preparation: Section 2.3 and 2.4 p.94
Review Exercises p.95

Chapter 3

Derivatives

3.1 Derivative of a Function Quick Review p.105
Exercises p.105
3.2 Differentiability Quick Review p.114
Exercises p.114
3.3 Rules for Differentiation Quick Review p.123
Exercises p.124
Quick Quiz for AP* Preparation: Section 3.1-3.3 p.126
3.4 Velocity and Other Rates of Change Quick Review p.135
Exercises p.135
3.5 Derivatives of Trigonometric Functions Quick Review p.146
Exercises p.146
3.6 Chain Rule Quick Review p.153
Exercises p.153
Quick Quiz for AP* Preparation: Section 3.4-3.6 p.156
3.7 Implicit Differentiation Quick Review p.162
Exercises p.162
3.8 Derivatives of Inverse Trigonometric Functions Exercises p.170
3.9 Derivatives of Exponential and Logarithmic Functions Quick Review p.178
Exercises p.178
Quick Quiz for AP* Preparation: Section 3.7-3.9 p.180
Review Exercises p.181

Chapter 4

Applications Of Derivatives

4.1 Extreme Values of Functions Quick Review p.193
Exercises p.193
4.2 Mean Value Theorem Quick Review p.202
Exercises p.202
4.3 Connecting f' and f'' with the Graph of f Quick Review p.214
Exercises p.215
Quick Quiz for AP* Preparation: Section 4.1-4.3 p.218
4.4 Modeling and Optimization Quick Review p.226
Exercises p.226
4.5 Linearization and Newton's Method Quick Review p.242
Exercises p.242
4.6 Related Rates Quick Review p.250
Exercises p.251
Quick Quiz for AP* Preparation: Section 4.4-4.6 p.255
Review Exercises p.256

Chapter 5

The Definite Integral

5.1 Estimating with Finite Sums Quick Review p.269
Exercises p.270
5.2 Definite Integrals Quick Review p.282
Exercises p.282
5.3 Definite Integrals and Antiderivatives Quick Review p.290
Exercises p.290
Quick Quiz for AP* Preparation: Section 5.1-5.3 p.293
5.4 Fundamental Theorem of Calculus Quick Review p.302
Exercises p.302
5.5 Trapezoidal Rule Quick Review p.311
Exercises p.312
Quick Quiz for AP* Preparation: Section 5.4-5.5 p.315
Review Exercises p.315

Chapter 6

Differential Equations And Mathematical Modeling

6.1 Slope Fields and Euler's Method Quick Review p.327
Exercises p.327
6.2 Antidifferentiation by Substitution Quick Review p.337
Exercises p.337
6.3 Antidifferentiation by Parts Quick Review p.346
Exercises p.346
Quick Quiz for AP* Preparation: Section 6.1-6.3 p.349
6.4 Exponential Growth and Decay Quick Review p.357
Exercises p.357
6.5 Logistic Growth Quick Review p.369
Exercises p.369
Quick Quiz for AP* Preparation: Section 6.4 and 6.5 p.372
Review Exercises p.373

Chapter 7

Applications Of Definite Integrals

7.1 Integral As Net Change Quick Review p.385
Exercises p.386
7.2 Areas in the Plane Quick Review p.395
Exercises p.395
7.3 Volumes Quick Review p.405
Exercises p.406
Quick Quiz for AP* Preparation: Section 7.1-7.3 p.411
7.4 Lengths of Curves Quick Review p.415
Exercises p.416
7.5 Applications from Science and Statistics Quick Review p.424
Exercises p.425
Quick Quiz for AP* Preparation: Section 7.4 and 7.5 p.429
Review Exercises p.430

Chapter 8

Sequences, Lhopital's Rule, And Improper Integrals

8.1 Sequences Quick Review p.440
Exercises p.441
8.2 L'Hopital's Rule Quick Review p.450
Exercises p.450
Quick Quiz for AP* Preparation: Section 8.1 and 8.2 p.452
8.3 Relative Rates of Growth Quick Review p.457
Exercises p.457
8.4 Improper Integrals Quick Review p.467
Exercises p.467
Quick Quiz for AP* Preparation: Section 8.3 and 8.4 p.470
Review Exercises p.470

Chapter 9

Infinite Series

9.1 Power Series Quick Review p.481
Exercises p.481
9.2 Taylor Series Quick Review p.492
Exercises p.492
9.3 Taylor's Theorem Quick Review p.500
Exercises p.500
Quick Quiz for AP* Preparation: Section 9.1-9.3 p.502
9.4 Radius of Convergence Quick Review p.510
Exercises p.511
9.5 Testing Convergence at Endpoints Quick Review p.522
Exercises p.523
Quick Quiz for AP* Preparation: Section 9.4 and 9.5 p.525
Review Exercises p.526

Chapter 10

Parametric, Vector, And Polar Functions

10.1 Parametric Functions Quick Review p.535
Exercises p.535
10.2 Vectors in the Plane Quick Review p.545
Exercises p.545
10.3 Polar Functions Quick Review p.557
Exercises p.557
Quick Quiz for AP* Preparation: Section 10.1-10.3 p.559
Review Exercises p.560
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