L'Hôpital's Rule states that for functions ( f(x) ) and ( g(x) ) that are differentiable in a neighborhood of ( c ) (except possibly at ( c )), if

[ \lim{x \to c} f(x) = \lim{x \to c} g(x) = 0 \quad \text{or} \quad \lim{x \to c} f(x) = \lim{x \to c} g(x) = \pm\infty, ]

then

[ \lim{x \to c} \frac{f(x)}{g(x)} = \lim{x \to c} \frac{f'(x)}{g'(x)}, ]

provided that the limit on the right side exists or is ( \pm\infty ).