Limits

1.1 Limits (Part 1)

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1.2 Limits (Part 2)

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1.3 Finding Asymptotes Using Limits

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1.4 Trigonometric Limits

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1.5 The Squeeze Theorem

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1.6 L'Hôpital's Rule

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1.7 Continuous Functions

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Applications of Derivatives

3.1 Position, Velocity, Acceleration

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3.2 Implicit Differentiation

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3.3 Related Rates

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Integrals

5.1 Antiderivatives and Basic Integration Rules

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5.2 Integration by Substitution

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5.3 Riemann Sums

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5.4 Definite Integrals

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5.5 First Fundamental Theorem of Calculus

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5.6 Second Fundamental Theorem of Calculus

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5.7 Average Value

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5.8 Functions Defined by Integrals

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Series

9.1 Sequences, Series, and Partial Sums

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9.2 Geometric Series, p-Series, and nth Term Test

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9.3 Direct Comparison, Limit Comparison, & Ratio Test

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9.4 Integral Test and Alternating Series Test

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Parametric Equations and Calculus

11.1 Parametric Equations

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11.2 Velocity and Acceleration Vectors

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11.3 Speed and Total Distance

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11.4 Slope of Tangent Line and Concavity

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Derivatives

2.1 Definition of the Derivative

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2.2 Average and Instantaneous Rate of Change

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2.3 Power, Chain, Product, and Quotient Rules

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2.4 Equations of Tangent and Normal Lines

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2.5 Derivatives of Logarithms and Exponentials

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2.6 Derivatives of Trigonometric Functions

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2.7 Inverse and Inverse Trigonometric Functions

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More Applications of Derivatives

4.1 Increasing and Decreasing Functions

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4.2 Extrema and Optimization

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4.3 Concavity and the Second Derivative

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4.4 Rolle's Theorem and Mean Value Theorem

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4.5 Linear Approximation

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Area and Volume Using Integration

6.1 Area Between Curves

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6.2 Volume by Cross-Section, Disks, and Washers

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Applications of Integrals

7.1 Separable Differential Equations

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7.2 Slope Fields and Euler's Method

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7.3 Growth and Decay

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7.4 Logistic Differential Equations

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Integration Techniques

8.1 Integration by Partial Fractions

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8.2 Integration by Parts

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8.3 Arc Length

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8.4 Improper Integrals and L'Hôpital's Rule

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Taylor and Maclaurin Series

10.1 Power Series/Radius and Interval of Convergence

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10.2 Maclaurin Series

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10.3 Lagrange Error Bound

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10.4 Taylor Series

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Polar Equations and Calculus

12.1 Polar Equations

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12.2 Derivatives of Polar Functions

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12.3 Area of Polar Curves

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12.4 Area Between Polar Curves

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