Let \( \alpha \) be a positive real number. Let \( f: R \rightarrow R \) and \( g:(\alpha, \inft...

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Let \( \alpha \) be a positive real number. Let \( f: R \rightarrow R \) and \( g:(\alpha, \infty) \rightarrow R \) be the functions defined by \( f(x)=\sin \left(\frac{\pi x}{12}\right) \) and \( g(x)=\frac{2 \log _{e}(\sqrt{x}-\sqrt{\alpha})}{\log _{e}\left(e^{\sqrt{x}}-e^{\sqrt{\alpha}}\right)} \)
Then the value of \( \lim _{x \rightarrow a^{+}} f(g(x)) \) is
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