Answer
$$1$$
Work Step by Step
\begin{aligned}
\lim _{x \rightarrow \pi} \sin \left(\frac{x}{2}+\sin x\right)&=\sin \left(\frac{\pi}{2}+\sin \pi\right)\\
&=\sin \left(\frac{\pi}{2}\right)\\
&=1
\end{aligned}
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 2: Limits and Continuity - Practice Exercises - Page 101: 21
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