Answer
$2$
Work Step by Step
Consider $f(x)=\int_{0}^{1} \dfrac{1}{\sqrt x} dx$
$\lim\limits_{a \to 0^{+}} f(x)= \lim\limits_{a \to 0^{+}} \int_{a}^{1} \dfrac{1}{\sqrt x} dx=\lim\limits_{a \to 0^{+}} [2 \sqrt x]_{a}^{1}$
or, $\lim\limits_{a \to 0^{+}} [2-2 \sqrt a]= 2$
