Limit involving Absolute Values.

**jpatrie** · October 10th 2008, 09:58 AM

$\lim_{y\rightarrow0}\frac{|3y-1|-|3y+1|}{y}$

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

**Plato** · October 10th 2008, 10:24 AM

$\frac{{ - 1}}<br /> {3} < y < \frac{1}<br /> {3} \Rightarrow \quad \frac{{\left| {3y - 1} \right| - \left| {3y + 1} \right|}}<br /> {y} = \frac{{\left( { - 3y + 1} \right) - \left( {3y + 1} \right)}}<br /> {y}$

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