Bah, after re-reading my post I guess it's not a very quick question. </edit>
So I just took a midterm, and one of the questions was as follows:
I found two ways to go about doing this.
1) divide all by x:
When you plug in +inf, you get:
Evaluating to -inf.
I checked this over at the end of the test though, and decided I didn't like this solution, as by the definition of a limit: the left side limit must equal the right side limit...and how do you evaluate the left and right side of infinity?
So, I erased that answer and proceeded to write answer #2:
So, for lim 1/x->0+, we have:
As lim lim
Which is -inf.
Also, for lim 1/x->0-, we have:
Which is +inf.
So, yah, a bunch of my friends all said -inf is right, but I really don't like the idea of putting that down as saying it is -inf implies the limit exists and approaches -inf, which isn't necessarily true, as inf isn't defined as a number....Aurgh.
lim1/x->0- DNE lim1/x->0+,
Therefore lim1/x->0 DNE.