The l'Hôpital's Rule

l'Hôpital's Rule. Suppose $f(x)$ and $g(x)$ are differentiable functions with $g'(x)\ne0$.

• If $\displaystyle\lim_{x\to a}f(x)=0=\lim_{x\to a}g(x)$, then $\displaystyle\lim_{x\to a}\frac{f(x)}{g(x)}=\lim_{x\to a}\frac{f'(x)}{g'(x)}$.
• If $\displaystyle\lim_{x\to a}f(x)=\pm\infty=\lim_{x\to a}g(x)$, then likewise $\displaystyle\lim_{x\to a}\frac{f(x)}{g(x)}=\lim_{x\to a}\frac{f'(x)}{g'(x)}$. …