# Real Analysis : Differentiability and Limits

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Prove : Assume f and g are continous functions defined on interval contaning a, and assume that f and g are differentiable on tis interval with the possible exception of the point a. If f(a)=0 and g(a)=0 then lim f'(x)/g'(x)=L as x->a implies lim f(x)/g(x)=L as x->a.

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Proof:

Since f(a)=0 and g(a)=0, according to the Mean value theorem, we ...

#### Solution Summary

Differentiability and limits are investigated.

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