Someone answered my question yesterday by saying $$ \lim_{x \to 0} {1 \over x} = \infty $$ but I think that it doesn't exist because $$\lim_{x \to 0^{+ }} \ne {\lim_{x \to 0^{-}}} $$ Am I right?

Question

Someone answered my question yesterday by saying $$ \lim_{x \to 0} {1 \over x}  = \infty $$ but I think that it doesn't exist because $$\lim_{x \to 0^{+ }} \ne {\lim_{x \to 0^{-}}} $$ Am I right?

anonymous · Answer

no the guy was right

parthkohli · Answer

How?

anonymous · Answer

what you are trying to prove you are looking for continuity :)

anonymous · Answer

if right and and left hand limits are equal then it is continuous.

parthkohli · Answer

But right hand limit is $-\infty$ and left hand limit is $+ \infty$.

parthkohli · Answer

They are different numbers

anonymous · Answer

you are right.
one sided limits exist for this function . i do not know the complete answer of that guy.
as a whole two sided limit does not exists for this .

anonymous · Answer

just remember this 
in order for the limit to exists . you reach that point from any direction it should give u the same result.

parthkohli · Answer

I already do :P

anonymous · Answer

in this case you can say that limit does not exists about zero for this function.

parthkohli · Answer

Heh—thank you!

anonymous · Answer

yw:)