Answer
$$\frac{1}{2}$$
Work Step by Step
\begin{align*}
\lim _{x \rightarrow \frac{\pi}{3}}\sin^2(\pi\sin^2x )&=\sin^2(\pi\sin^2\frac{\pi}{3} )\\
&=\sin^2(\pi\frac{3}{4})\\
&=\frac{1}{2}.
\end{align*}
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 2 - Limits - 2.4 Limits and Continuity - Exercises - Page 68: 79
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