How to Calculate a Limit Using Cauchy's Mean Value Theorem?
Thread startertransgalactic
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In summary: I almost said what you wrote but I don't know what you wrote!) It is not at all clear to me that, even with the additional information, the limit exists. You can easily construct examples where, even though f and g are differentiable at 0, f'(x) and g'(x) are not differentiable at 0. I think you are going to have to look at the definition of the derivative and see if you can prove that the limit exists. I would start by looking at the Weierstrass definition although knowing the "mean value theorem" might be useful.f(x) and g(x) are differentiable on 0f(0)=g(0)=0
