Answer
$4$
Work Step by Step
Consider $f(x)=\int_{0}^{4} \dfrac{1}{\sqrt {4-x}} dx$
$\lim\limits_{a \to 4^{-}} f(x)= \lim\limits_{a \to 4^{-}} \int_{0}^{a} \dfrac{1}{\sqrt {4-x}} dx=\lim\limits_{a \to 4^{-}} [-2 \sqrt {4-x}]_{0}^{a}$
or, $\lim\limits_{a \to 4^{-}} [-2 \sqrt {4-a}+4]= 4$
