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RE: Limits: Is there something I'm missing Here?
Ashraf, Strictly speaking you are correct. The limit does not exist. But there is such a thing as a one-sided limit, which is not a true limit but still useful. In this case even the one-sided limits do not really exist because the result is unbounded. But again, it is useful to signify this by saying that the limit is infinite. So it is rather loose language by both mathematicians and Mathematica. Perhaps one of the mathematicians in the group will give you a fuller explanation. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: Ashraf El Ansary [mailto:Elansary at btopenworld.com] To: mathgroup at smc.vnet.net Dear all, One thing I've noticed that if we have a function which has two different limits (given two different directions) at one points , mathematica would be still give an answer though to my understanding the limit doesn't exist in such a case. Consider the following example: a[x_]:=1/x Limit[a[x],x->0,Direction->+1] +Inf Limit[a[x],x->0,Direction->+1] -Inf Limit[a[x],x->0]. +Inf.... Maybe my calculus knowledge is a bit rusty but does the limit exist in this case?? Thank you