Chapter B, Problem 20E

To determine

Whether the statement “Suppose f and g satisfy the hypothesis for l’Hôpital’s Rule. If $\underset{x\to a}{\lim }f\left(x\right)=\underset{x\to a}{\lim }g\left(x\right)=0$ then $\underset{x\to a}{\lim }\frac{f\left(x\right)}{g\left(x\right)}=\underset{x\to a}{\lim }\frac{d}{dx}\left[\frac{f\left(x\right)}{g\left(x\right)}\right]$”is true or false.