Lim x-->0-: 2/x Does Not Exist

[Miike012]

Lim 1/x - 1/abs(x)
x -->0-

= 2/x

as x approaches 0- , 2/x approaches neg infinity...

why isn't this correct? the answer is does not exist.

 

[verty]

What is the limit from the right?

 

[HallsofIvy]

That is right. "Infinity" is not a number. Saying that a limit is "infinity" or "negative infinity" is just saying that the limit does not exist for a particular reason.

verty, the limit from the right is not relevant. The problem specifically asks for the limit from the left: $\lim_{x\to 0^-}$.

 

[verty]

I apologise, I thought Mike was asking, why isn't this the limit, but he meant, why isn't this the one-sided limit.