Mathematics - Limits Question with Solution | TestHub

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