Showing a limit does not exist?

I cheated by looking at a graph and it goes to , but when I try to solve it algbraically by substitution, I plug in and get undefined in the denominator, as I'd expect with an infinite limit. But how do I show the algebraic work that the behavior of the function as the goes to both ?

Re: Showing a limit does not exist?

Quote:

Originally Posted by

**LiberalArtMajorTakingCalc**
I cheated by looking at a graph and it goes to

, but when I try to solve it algbraically by substitution, I plug

in and get undefined in the denominator, as I'd expect with an infinite limit. But how do I show the algebraic work that the behavior of the function as the

goes to both

?

Let define

It is clear that , but .

Re: Showing a limit does not exist?

Where did and come from?