Calculus Notes and Example Problems
Each link is a pdf document.
Key topics in each document are noted with bulletpoints.
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- Rate of Change
- Secant Line
- Tangent Line
- Average Rate of Change
- Definition of Derivative
- Instantaneous Rate of Change
- Equation of Tangent Line
- One Sided Limits
- Using Graphs to Find Limits
- Estimating Limits Numerically Using Tables
- Evaluating Limits
- Infinite Limits
- Limits at Infinity
- Squeeze Theorem
- Trigonometric Limits
- L'Hopital's Rule
Continuity and Differentiability
- Three Conditions for Continuity
- Types of Discontinuity
- Three Ways a Function is Not Differentiable
- Derivative Notation
- Notation for Chain Rule
- General Power Rule
Maximum, Minimum, and Concavity
- Absolute Max and Min
- Local Max and Min
- First Derivative Test
- Intervals of Increase, Decrease
- Critical Numbers
- Concavity and Points of Inflection
- Second Derivative Test
Integration Rules and Properties
- Indefinite Integrals
- Antiderivatives
- u-substitution