Use algebra to evaluate the limit exactly.
lim(h->0) (1/(a+h) - 1/a)/h
I saw you there, Jhevon. Beat you on this one . I'm gonna go back and edit now
And here's the edit:
Get a common denominator:
$\displaystyle \frac{1}{a+h} - \frac{1}{a} = \frac{a}{a(a + h)} - \frac{a+h}{(a+h)a}$
Simplify:
$\displaystyle = \frac{a - (a + h)}{a(a + h)} = \frac{-h}{a(a + h)}$.
Therefore:
$\displaystyle \frac{\frac{1}{a+h} - \frac{1}{a}}{h} = \frac{-1}{a(a + h)}$.
The limit should now be obvious.