# Limit involving Absolute Values.

• Oct 10th 2008, 10:58 AM
jpatrie
Limit involving Absolute Values.
$\lim_{y\rightarrow0}\frac{|3y-1|-|3y+1|}{y}$

The only way I can think of getting an answer is substituting values close to 0, but can anyone show me how to do it definitively.

Thanks
• Oct 10th 2008, 11:24 AM
Plato
$\frac{{ - 1}}
{3} < y < \frac{1}
{3} \Rightarrow \quad \frac{{\left| {3y - 1} \right| - \left| {3y + 1} \right|}}
{y} = \frac{{\left( { - 3y + 1} \right) - \left( {3y + 1} \right)}}
{y}$