Question

$\underset{x\to 0}{\lim }\frac{3^{2+x}-9}{x}$

Answer 1

$$\begin{gathered} \underset{x\to 0}{\lim }\left[\frac{3^{2+x}-9}{x}\right] \\ =\underset{x\to 0}{\lim }\left[\frac{3^2·3^x-3^2}{x}\right] \\ =3^2\underset{x\to 0}{\lim }\left[\frac{3^x-1}{x}\right] \\ =9\log \left(3\right) \\ =9{\log }_{e}3 \end{gathered}$$