Answer
(a) $\sqrt{a+h}-\sqrt{a}$
(b) $\frac{1}{\sqrt{a+h}+\sqrt{a}}$
Work Step by Step
We are given: $f(t)=\sqrt{t}$; $t=a$, $t=a+h$
(a) We calculate the net change:
$f(a+h)-f(a)=\sqrt{a+h}-\sqrt{a}$
(b) We calculate the average rate of change:
$\displaystyle \frac{f(a+h)-f(a)}{(a+h)-a}=\frac{\sqrt{a+h}-\sqrt{a}}{h}*\frac{\sqrt{a+h}+\sqrt{a}}{\sqrt{a+h}+\sqrt{a}}=\frac{(a+h)-a}{h(\sqrt{a+h}+\sqrt{a})}=\frac{h}{h(\sqrt{a+h}+\sqrt{a})}=\frac{1}{\sqrt{a+h}+\sqrt{a}}$
