LHopitals_Rule

Let $f$ and $g$ be real functions which are continuous on the closed interval $\closedint a b$ and differentiable on the open interval $\openint a b$. Let $\forall x \in \openint a b: \map {g'} x \ne 0$ where $g'$ denotes the derivative of $g$ $x$. Let $\map f a = \map g a = 0$ Then $\displaystyle \lim_{x \mathop \to a^+} \frac {\map f x} {\map g x} = \lim_{x \mathop \to a^+} \frac {\map {f'} x} {\map {g'} x}$ provided that the second limit exists.