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