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Definition and Properties of Limits for AP Calculus

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By — McGraw-Hill Professional
Updated on Oct 24, 2011

Practice problems for this concept can be found at Limits and Continuity Practice Problems for AP Calculus.

Definition of Limit

Let f be a function defined on an open interval containing a, except possibly at a itself. Then (read as the limit of f (x) as x approaches a is L) if for any ε > 0, there exists a δ > 0 such that | f (x) – L| < ε whenever |x – a| < δ.

Properties of Limits

Given and and L, M, a, c, and n are real numbers, then:

Practice problems for this concept can be found at Limits and Continuity Practice Problems for AP Calculus.

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