lim |x| / x

x-> 0

How would I begin to solve this?

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- Sep 16th 2011, 09:19 AMhabibixoxLimits of absolute value.
lim |x| / x

x-> 0

How would I begin to solve this? - Sep 16th 2011, 09:22 AMProve ItRe: Limits of absolute value.
- Sep 16th 2011, 09:24 AMTheChazRe: 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, 09:33 AMhabibixoxRe: Limits of absolute value.
Therefore the limit doesn't exist since the left and right are not equal right?

- Sep 16th 2011, 09:36 AMProve ItRe: Limits of absolute value.