# Continuity Proof

Assume that f(x) is continuous in some open interval J that contains the point a, f'(x) exists for each x and limit of f'(x) as xa exists. Prove that f is differentiable at a and

f'(a)=limit of f'(x) as xa

keywords: differentiability

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Assume that f(x) is continuous in some open interval J that contains the point a,

f'(x) exists for each x and limit of f'(x) as xa exists. ...

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A continuity proof is provided. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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