When does the limit not exist?!?

Question

hartnn · Answer

when left hand limit does not = right hand limit
know what those are ?

anonymous · Answer

Example?

nory · Answer

Suppose you have a function like this:
|dw:1378960240675:dw|
It has an asymptote at x=0.
Well what is the limit as x goes to 0? Is it infinity? Or is it negative infinity? You can't tell. As you close in on 0 from the right side, it goes to positive infinity, but from the left side, to negative infinity.
That's an intuitive view of the matter.

hartnn · Answer

$\lim \limits_{x->0^-} \frac{\sin x}{x}$

hartnn · Answer

is the left hand limit

nory · Answer

@izhangy good question.

hartnn · Answer

i think nory explained it better :)

nory · Answer

I like your example, though.
But I thought that limit was 1? Maybe I'm wrong. But I seem to remember them making a big deal out of a similar limit when I took calculus.

anonymous · Answer

Ah, i understand now, thanks guys.

hartnn · Answer

that limit exist and is =1
hence both left hand limit = right hand limit =1