Question

use one sided limits at x->3 from the right and left to fin the lim

x^2-9/(abs(x-3))

Answer 1

I will do the limit from the left side, and leave to you the other part:
\[\lim_{x \rightarrow 3^-}{x^2-9 \over \left| x-3 \right|}=\lim_{x \rightarrow 3^-}{(x+3)(x-3) \over -(x-3)}=\lim_{x \rightarrow 3^-}-(x+3)=-6\]

Answer 2

ok so in the denom what do you do for the right side?

Answer 3

like how did you know to put a - sign in front?

Answer 4

if we are looking to left of 3, then we are looking at numbers smaller than 3
x<3=>|x-3|=-(x-3)

Answer 5

if you are looking to the right of 3, then we are looking at numbers greater than 3
x>3=>|x-3|=x-3

Answer 6

oh alright i have never done it that way