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    Continuity Proof

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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 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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    https://brainmass.com/math/discrete-math/continuity-proof-intervals-85851

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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 xa 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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