Answer
$\lim\limits_{h \to 0}\frac{\sqrt {5h+4} -2}{h} = 1.25=\frac{5}{4}$
Work Step by Step
$\frac{\sqrt (5h+4) -2}{h}= \frac{(\sqrt (5h+4) -2)(\sqrt (5h+4) +2)}{h(\sqrt (5h+4) +2)}$
= $\frac{ (5h+4) -4)}{h(\sqrt (5h+4) +2)}$
= $\frac{ (5h)}{h(\sqrt (5h+4) +2)}$
= $\frac{5}{(\sqrt (5h+4) +2)}$
Now, we apply the property of limits:
$\lim\limits_{h \to 0}\frac{5}{(\sqrt (5h+4) +2)} = \frac{\lim\limits_{h \to 0}5}{\lim\limits_{h \to 0}(\sqrt (5h+4) +2)}$
= $\frac{5}{4}$ = 1.25
