# Thread: Evaluate limit of a absolute value

1. ## Evaluate limit of a absolute value

lim as x goes to 0

(abs(2x-1)-abs(2x+1))/x

Something with piecewise?

2. For $\displaystyle 0<x<\frac{1}{2}$ is $\displaystyle |2x-1|= 1-2x$ and $\displaystyle |2x+1|= 2x+1$ so that is...

$\displaystyle \displaystyle \lim_{x \rightarrow 0+} \frac {|2x-1|- |2x+1|}{x} = \lim_{x \rightarrow 0+} \frac {-4x}{x} = -4$ (1)

For $\displaystyle -\frac{1}{2}<x<0$ is [also]$\displaystyle |2x-1|= 1-2x$ and $\displaystyle |2x+1|= 2x+1$ so that is...

$\displaystyle \displaystyle \lim_{x \rightarrow 0-} \frac {|2x-1|- |2x+1|}{x} = \lim_{x \rightarrow 0-} \frac {-4x}{x} = -4$ (2)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$