Thread: Limits of absolute value.

lim |x| / x
x-> 0



How would I begin to solve this?

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 and then see what happens as you approach 0 from the left and from the right...

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

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

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.