# Limits of absolute value.

• Sep 16th 2011, 08:19 AM
habibixox
Limits of absolute value.
lim |x| / x
x-> 0

How would I begin to solve this?
• Sep 16th 2011, 08:22 AM
Prove It
Re: Limits of absolute value.
Quote:

Originally Posted by habibixox
lim |x| / x
x-> 0

How would I begin to solve this?

Start by making use of the definition of the absolute value $\displaystyle \displaystyle |x| = \begin{cases} \phantom{-}x \textrm{ if }x \geq 0 \\ -x\textrm{ if }x < 0\end{cases}$ and then see what happens as you approach 0 from the left and from the right...
• Sep 16th 2011, 08:24 AM
TheChaz
Re: Limits of absolute value.
Use the definition of absolute value.
As x -> 0+
(from the right)
It is true that x is positive, so |x| is just x

So you have x/x when x is positive
-x/x when x is negative.

Ie f(x) = 1 when x > 0
f(x) = -1 when x < 0
• Sep 16th 2011, 08:33 AM
habibixox
Re: Limits of absolute value.
Therefore the limit doesn't exist since the left and right are not equal right?
• Sep 16th 2011, 08:36 AM
Prove It
Re: Limits of absolute value.
Quote:

Originally Posted by habibixox
Therefore the limit doesn't exist since the left and right are not equal right?

"Since the left and right hand LIMITS are not equal", yes.