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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
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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
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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
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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
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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
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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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