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Let f : [tex]\Re[/tex][tex]\rightarrow[/tex][tex]\Re[/tex] be a continuous function that is differentiable for all nonzero x such that f '(x) exists. If f'(x) [tex]\rightarrow[/tex] L as x[tex]\rightarrow[/tex]0 exists, prove that f '(0) exists.

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# Proving that f'(0) exists

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