Answer
$0$
Work Step by Step
\begin{align*}
\lim _{t \rightarrow 0} \frac{ \sin^2 t}{t}&=\lim _{t \rightarrow 0} \frac{\sin t}{t}\sin t\\
&=\lim _{t \rightarrow 0} \frac{\sin t}{t}\lim _{t \rightarrow 0}\sin t\\
&=0.
\end{align*}
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