# Find this limit

• Mar 29th 2011, 07:22 PM
LandLBoy
Find this limit
(x^-2 - 3^-2)/ (x-3)

find the limit as x approaches 3

i've tried changing the exponents into radical form so i can multiply the top and bottom by the conjugate but i can't seem to make it work.. can someone solve this for me please?
• Mar 29th 2011, 07:26 PM
Prove It
$\displaystyle \frac{x^{-2} - 3^{-2}}{x - 3} = \frac{\frac{1}{x^2} - \frac{1}{3^2}}{x - 3}$

$\displaystyle = \frac{\frac{3^2 - x^2}{3^2x^2}}{x - 3}$

$\displaystyle = \frac{(3 - x)(3 + x)}{3^2x^2(x - 3)}$

$\displaystyle = \frac{-(x - 3)(3 + x)}{3^2x^2(x - 3)}$.

Go from here.