Answer
$$- \frac{9}{2}.$$
Work Step by Step
\begin{align*}
\lim _{h \rightarrow 0}\frac{\cos 3 h-1}{h^2}&= \lim _{h \rightarrow 0}9 \frac{\cos 3 h-1}{(3h)^2}\\
&= - 9\lim _{3h \rightarrow 0} \frac{1-\cos 3 h}{(3h)^2}\\
&=- \frac{9}{2}.\\
\end{align*}
Where we used the fact that $\lim _{h \rightarrow 0} \frac{1-\cos h}{h^2}=\frac{1}{2}$.
