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Calculate the limit:

$$\lim _{ x\rightarrow \pi }{ \frac { \sin(x)-\cos\left( \frac { x }{ 2 } \right) }{ { x }^{ 2 }-\pi x } } $$

A

The limit does not exist.

B

$1$

C

$-\cfrac {1}{2\pi}$

D

$\cfrac {3}{2\pi}$

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