l'Hopital's rule

Let $f, g$ be differentiable functions on an interval $I$ containing real number $c$ , such that $g^{'} (x) \neq 0$ for $x \in I ∖ {c}$ .

If either

lim_{x \to c} f (x) = lim_{x \to c} g (x) = 0

lim_{x \to c} | f (x) | = lim_{x \to c} | g (x) | = \infty

then

lim_{x \to c} \frac{f (x)}{g (x)} = lim_{x \to c} \frac{f^{'} (x)}{g^{'} (x)} = L

for the limit $L$ .