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.Code:lim (1-x^2) x->+inf ------- (3+x)
1) divide all by x:
When you plug in +inf, you get:Code:lim (1-x^2)/x x->+inf ------- (3+x)/x lim (1/x-x) x->+inf ------- (3/x+1)
Evaluating to -inf.Code:-inf ---- 1
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:Code:lim (1-x^2) x->+inf ------- (3+x) As lim lim x->+inf 1/x->0. Therefore, lim (1-(1/x)^2) 1/x->0 ---------- (3+(1/x))
Which is -inf.Code:-inf ---- +inf
Also, for lim 1/x->0-, we have:
Which is +inf.Code:-inf ---- -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.Code:lim1/x->0- DNE lim1/x->0+, Therefore lim1/x->0 DNE.