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Let the real-valued function

$$f(x)=\begin{cases} \left|{\sin\frac{\pi}{2x}}\right|^{x},& x>0\, \text{ and } x\neq\frac{1}{2n}, \;n\in\mathbb{N}\\ 1,& x=\frac{1}{2n},\; n\in\mathbb{N}\;. \end{cases}$$

Find, if it exists, $\displaystyle\mathop{\lim}\limits_{x\rightarrow{0^{+}}}{f(x)}$.

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