lim x->3 ((x^-2)-(3^-2))/(x-3)

Answer 1

I see it as
lim [1/x^2 - 1/9]/(x-3) as x-->3
using a common denominator of 9x^2 and adding up the square bracket, we get
lim[(9-x^2)/(9x^2)]/(x-3)
= lim[(3-x)(3+x)/9x^2]/(x-3)
= lim [-(3+x)/9x2] as x --> 3
= -6/81 = -2/27

Answer 2

Wow, this was complicated. Had to draw everything out and look at it a few times. Thank you very much! :D