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AP Calculus AB/Unit 1: Limits and Continuity
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Definition of Continuity at a Point

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If lim⁡x→af(x)=f(a)\displaystyle \lim_{x \to a} f(x) = f(a), which of the following statements about the function ff must be true?

A

The line y=f(a)y = f(a) is tangent to the graph of ff at x=ax = a.

B

ff is continuous at x=ax = a.

C

ff is differentiable at x=ax = a.

D

For all values of xx, f(x)=f(a)f(x) = f(a).

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