Answer
$1$
Work Step by Step
Here, $\lim\limits_{x \to 0^{+}} f(x)=\lim\limits_{x \to \infty} \dfrac{\sqrt {x}}{\sqrt {\sin x}}$
This implies that
$\lim\limits_{x \to \infty} \dfrac{\sqrt {x}}{\sqrt {\sin x}}=\sqrt{\lim\limits_{x \to 0^{+}} \dfrac{x}{\sin x}}$
or, $ \sqrt{ \dfrac{1}{\lim\limits_{x \to 0^{+}}(\sin x/x)}}=\sqrt {\dfrac{1}{1}}=1$
