Originally Posted by
Bacterius As General said, you are left with :
$\displaystyle \lim_{h\to0} \frac{\sqrt{7(a+h)} - \sqrt{7a} }{h} \frac{\sqrt{7(a+h)} + \sqrt{7a}}{\sqrt{7(a+h)} + \sqrt{7a}}$
This might look impressive at first, but take the top part of the fraction :
$\displaystyle (\sqrt{7(a+h)} - \sqrt{7a} )(\sqrt{7(a+h)} + \sqrt{7a})$.
This can be simplified to $\displaystyle 7(a+h) - 7a = 7(a + h - a) = 7h$. So your limit basically boils down to :
$\displaystyle \lim_{h\to0} \frac{7h}{h(\sqrt{7(a+h)} + \sqrt{7a})}$
Cancel the $\displaystyle h$, and you are pretty much done.