AP Calculus BC Knowledge Review: Limits and Continuity

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Introduce:

On the AP Calculus BC exam, you will be tested on your ability to find the limit of a function. In this chapter, you will be shown how to solve several types of limit problems, which include finding the limit of a function as x approaches a specific value, finding the limit of a function as x approaches infinity, one-sided limits, infinite limits, and limits involving sine and cosine. You will also learn how to apply the concepts of limits to finding vertical and horizontal asymptotes as well as determining the continuity of a function.

Key Ideas

Definition of the limit of a function

Properties of limits

Evaluating limits as x approaches a specific value

Evaluating limits as x approaches ± infinity

One-sided limits

Limits involving infinities

Limits involving sine and cosine

Vertical and horizontal asymptotes

Continuity

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