# Calculus Lessons

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## Limits

- Evaluating the Limit of a Function at a Point Graphically
- Evaluating the Limit of a Function at a Point Algebraically
- Algebraic Techniques to Evaluate Limits When the Denominator Equals Zero
- Limits Involving Infinity (Answer Equals Infinity)
- Limits Involving Infinity (Limit Approaches Infinity)
- Limits of Trigonometric Functions
- Continuity

## Derivatives

- Definition of the Derivative
- Basic Differentiation Rules
- Product Rule and Quotient Rule
- Derivatives of Trigonometric Functions
- Proofs of Derivatives of Trigonometric Functions
- Chain Rule
- Implicit Differentiation
- Higher Order Derivatives
- L'Hopital's Rule

## Applications of Derivatives

- Equations of Tangent and Normal Lines to a Curve
- Velocity and Acceleration
- Related Rates
- Relationship Between Continuity and Differentiability
- Rolle's Theorem
- Mean Value Theorem
- Critical Points
- Increasing and Decreasing Functions and the First Derivative Test
- Concavity and the Second Derivative Test
- Optimization Problems
- Curve Sketching (Part 1)
- Curve Sketching (Part 2)
- Newton's Method

## Applications of Definite Integrals

- Areas of Regions Between Curves
- Finding Volumes of Solids Using the Disk Method
- Finding Volumes of Solids Using the Washer Method
- Finding Volumes of Solids Using the Shell Method

## Integration

## Applications of Integration

- Areas of Regions Between Curves
- Finding Volumes of Solids Using the Disk Method
- Finding Volumes of Solids Using the Washer Method
- Finding Volumes of Solids Using the Shell Method
- Arc Length
- Areas of Surfaces of Revolution

## Transcendental Functions

- Inverse Functions - Differentiation and Integration
- Natural Logarithms - Differentiation and Integration
- Exponential Functions - Differentiation and Integration
- Other Exponential and Logarithmic Functions - Differentiation and Integration
- Exponential Growth and Decay
- Inverse Trigonometric Functions
- Inverse Trigonometric Functions - Differentiation
- Inverse Trigonometric Functions - Integration
- Hyperbolic Functions

## Techniques of Integration

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