Answer
$$\lim_{t\to0}\frac{t^3}{\tan^32t}$$
Work Step by Step
Given
$$\lim_{t\to0}\frac{t^3}{\tan^32t}$$
Since $$ \lim_{t\to0}\frac{0^3}{\tan^32(0)}=\frac{0}{0}$$
then
\begin{align*}
\lim_{t\to0}\frac{t^3}{\tan^32t}&=\lim_{t\to0}\frac{1}{\frac{\tan^32t}{t^3}}\\
&=\frac{\lim_{t\to0}1}{\lim_{t\to0}\frac{\tan^32t}{t^3}}\\
&=\frac{\lim_{t\to0}1}{\left(2\lim_{2t\to0}\frac{\tan 2t}{2t }\right)^3}\\
&=\frac{1}{8}
\end{align*}