L'Hopital's Rule

Definition

Let $f$ and $g$ be differentiable at all points in some open interval containing $x=c$ (except possibly at $c$). If ${\lim }_{x\to c}f(x)={\lim }_{x\to c}g(x)=0\text{ or }\infty$then ${\lim }_{x\to c}\frac{f(x)}{g(x)}={\lim }_{x\to c}\frac{f^{\prime }(x)}{g^{\prime }(x)}$Provided the limit on the right exists, or equals $\infty$ or $-\infty$ This result also holds

1. for limits at infinity, i.e. $c=\pm \infty$
2. for one-sided limits