Evaluate the limit below for $f(t) = \sqrt{t}$ and $x = 4$ in two steps by using algebra to simplify the difference quotient and then evaluating the limit.

$\displaystyle \lim_{h \to 0} \Bigg( \frac{f(x+h)-f(x)}{h} \Bigg) = \lim_{h \to 0} \Bigg($ $\Bigg) =$ .