# Thread: Limits of absolute value.

1. ## Limits of absolute value.

lim |x| / x
x-> 0

How would I begin to solve this?

2. ## Re: Limits of absolute value.

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 $\displaystyle |x| = \begin{cases} \phantom{-}x \textrm{ if }x \geq 0 \\ -x\textrm{ if }x < 0\end{cases}$ and then see what happens as you approach 0 from the left and from the right...

3. ## 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

4. ## Re: Limits of absolute value.

Therefore the limit doesn't exist since the left and right are not equal right?

5. ## Re: Limits of absolute value.

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.