Answer
$$\frac{1}{3}$$
Work Step by Step
\begin{align*}
\lim _{x \rightarrow -\frac{\pi}{2}} 3^{\sin x}&= 3^{\sin -\frac{\pi}{2} }\\
&= 3^{-1}\\
&=\frac{1}{3}.
\end{align*}
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