lim f(X)= (sq root x+5)-3/(x)
x-> 0

Just checking, but is that \lim_{x\to 0}\frac{\sqrt{x+5}-3}{x}

or

\lim_{x\to 0}\sqrt{x+5}-\frac{3}{x}

or

\lim_{x\to 0}\sqrt{x}+5-\frac{3}{x}

In any case, the limit does not exist.

For instance, in the first case, as we approach 0 from the right, we get {\infty}

As we approach 0 from the left, we get -\infty

lim (1/x)-(1/2)
x-->2 -------------------
(x-2)