# Math Help - Absolute value limits

1. ## Absolute value limits

Can someone please refresh my memory as to how I'd solve down on an equation as such? I seem to be quite foggy with pre-calc. :/

$lim x->2$
$|x-2|$
____________________
$x-2$

_______= divided by. :P

2. Originally Posted by jimmyp
Can someone please refresh my memory as to how I'd solve down on an equation as such? I seem to be quite foggy with pre-calc. :/

$lim x->2$
$|x-2|$
____________________
$x-2$

_______= divided by. :P

If you mean

$\lim_{x \to 2}\frac{|x-2|}{x-2}$

This limit does not exist.

The limit from the left is

$\lim_{x \to 2^-}\frac{2-x}{x-2}=-1$

The limit from the right is

$\lim_{x \to 2^+}\frac{x-2}{x-2}=1$

Since the left and right limits are not equal the limit does not exist.