Example 10. Find $\lim _{x \rightarrow 0}\left(\frac{\sin 3 x}{x}\right)^{x+2}$.
Solution. This is a limit of the form (1.60), where $\varphi(x)=\frac{\sin 3 x}{x}, \psi(x)=x+2$.

From (1.67)

$$
\lim _{x \rightarrow 0} \frac{\sin 3 x}{x}=3, \lim _{x \rightarrow 0}(x+2)=2
$$

According to formula (1.62), we get

$$
\lim _{x \rightarrow 0}\left(\frac{\sin 3 x}{x}\right)^{x+2}=3^{2}=9
$$