L'Hpital's Rule in its 1696 form said this: if lim x a f(x) = lim x

Question:

L'Hpital's Rule in its 1696 form said this: if lim x → a f(x) = lim x → a g(x) = 0, then lim x → a f(x) /g(x) = f'(a) /g' (a). provided that f' (a) and g' (a) both exist and g'(a) ( 0. Prove this result whiteout recourse to Cauchy's Mean Value Theorem?