Question

question below

Answer 1

\[\lim_{x \rightarrow 3}\frac{ \left| x-3 \right| }{ x^2-9 }\]
I know that the limit doesn't exist for this, but I'm wondering why.

Answer 2

seems unlikely doesn't it?

Answer 3

if \(x>3\) then this is the same as
\[\frac{x-3}{(x+3)(x-3)}=\frac{1}{x+3}\]

Answer 4

otoh if \(x<3\) it is the same as
\[\frac{3-x}{(x+3)(x-3)}=-\frac{1}{x+3}\]

Answer 5

alright I think I've got it, thanks @satellite73