Answer
$\dfrac{1}{2}$
Work Step by Step
Here, $\lim\limits_{y \to 0} f(0)=\dfrac{0}{0}$
This shows an indeterminate form of limit, thus we will apply L-Hospital's rule such as:
$\lim\limits_{x \to \infty} f(x)=\lim\limits_{x \to \infty} \dfrac{p'(x)}{q'(x)}$
we have $p'(x)=\dfrac{1}{2}(5y+25)^{-1/2}(5)=\dfrac{5}{2(5+25)^{1/2}}$ and $q'(x)=1$
$ \lim\limits_{y \to 0} \dfrac{\dfrac{5}{2(5+25)^{1/2}}}{1}=\dfrac{5}{2\sqrt {5(0)+25}}$
or, $\dfrac{5}{10}=\dfrac{1}{2}$
