Suppose that an object is at position s(t)= sqrt(t) feet at time t seconds.

 the average velocity of the object over a time interval from time 4+h seconds to time 4 seconds is 

$\frac{S(4+h）-S(4)}{(h+4)-4}=\frac{（\sqrt{4+h}-\sqrt{4})}{h}=\frac{（\sqrt{4+h}-\sqrt{4})}{h}*\frac{\sqrt{4+h}+\sqrt{4}}{\sqrt{4+h}+\sqrt{4}}=\frac{h}{h*(\sqrt{4+h}+\sqrt{4})}=1/(\sqrt{4+h}+\sqrt{4})$

(2)$\lim_{h\rightarrow 0} 1/(\sqrt{4+h}+\sqrt{4})=1/(\sqrt{4}+\sqrt{4})=1/2$