## Calculus (3rd Edition)

L’Hôpital’s Rule does not apply and the limit is $0$.
Since we have $$\lim _{x \rightarrow 0} \frac{\sin 4x}{x^{2}+3x+1}=\frac{0}{1}=0.$$ then L’Hôpital’s Rule does not apply and the limit is $0$.