Many calculus concepts are developed by first considering a discrete model and then the consequences of a limiting case. Therefore, the idea of limits is essential for discovering and developing important ideas, definitions, formulas, and theorems in calculus. Students must have a solid, intuitive understanding of limits and be able to compute various limits, including one-sided limits, limits at infinity, the limit of a sequence, and infinite limits. They should be able to work with tables and graphs in order to estimate the limit of a function at a point. Students should know the algebraic properties of limits and techniques for finding limits of indeterminate forms, and they should be able to apply limits to understand the behavior of a function near a point. Students must also understand how limits are used to determine continuity, a fundamental property of functions.

Click on a link to jump ahead to the following sections:

- Lesson 1: Rates of Change and Tangent Lines
- Advantage In - complete lesson

- Lesson 2: Introduction to Limits
- Close Enough - complete lesson

- Lesson 3: Calculating Limits
- Limits - complete lesson

- Lesson 4: Limits Involving Infinity
- Limits Involving Infinity - complete lesson on Asymptotes and End Behavior
- Video - NancyPi video on YouTube

- Lesson 5: Continuity
- Continuous Functions - complete lesson on Continuity

- Lesson 6: Assessment
- AP Practice - Multiple Choice problems from previous AP exams
**Supplemental Tasks:**- Blueberry Pancake Recipe with limits
- Limits of Piecewise Functions - Try to evaluate the one-sided limits of the piecewise functions in the GeoGebra app below.

The following are links to resources for Limits:

- Limits and Continuity - Entire unit on Khan Academy
- Calculating Limits - A concise summary of the different methods used in evaluating limits

The following are other free resources:

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