Question

Evaluate:

$\underset{x\to \infty }{lim}\frac{2+\sin x}{x^2+3}$.

Answer 1

By using D.L. hospital rule

$$\begin{array}{c}{lim}_{x\to \infty }\frac{\cos x}{2x}=\frac{\infty }{\infty }\\ {lim}_{x\to \infty }\frac{-\sin x}{2}\\ =-\infty \end{array}$$