Answer
$0$
Work Step by Step
Consider $f(x)=\lim\limits_{x \to 0^{+}} \sqrt x \sec
x=\lim\limits_{x \to 0^{+}}\dfrac{\sqrt x}{\cos x}=\lim\limits_{k \to 0^{+}} \dfrac{a(x)}{b(x)}$ and $a(0)=0, b(0) \ne 0$
Thus, $f(0) \ne \dfrac{0}{0}$
This shows an Inderminate form of the limit, so apply L-Hospital's rule:
$\lim\limits_{x \to l}\dfrac{a(x)}{b(x)}=\lim\limits_{x \to l}\dfrac{a'(x)}{b'(x)}$
Thus,
$\lim\limits_{x \to 0^{+}}\dfrac{\sqrt x}{\cos x}=0$
