Verify Lagrange's mean-value theorem for the following function:
$f(x)=\sin x$ on $\left[\frac{\pi}{2}, \frac{5 \pi}{2}\right]$
$\mathrm{x}=\frac{\mathrm{n} \pi}{2}, \mathrm{n} \in\{1,2,3,4,5\}$
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