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Re: Limits: Is there something I'm missing Here?
"Ashraf El Ansary" <Elansary at btopenworld.com> wrote: > 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. You're correct. Mathematica _sometimes_ does that. And I think that behavior can be terribly deceptive to a naive user! > Consider the following example: > a[x_]:=1/x > > Limit[a[x],x->0,Direction->+1] +Inf You had probably intended to write 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?? That depends. In an ordinary calculus course, yes, we'd normally just say that the limit doesn't exist. But a perfect answer should be available to Mathematica: ComplexInfinity If Mathematica doesn't give that, then no answer would be preferable to giving +Infinity, in my opinion. BTW, it amazes me that Mathematica can't even do something as simple as Limit[Floor[x], x->0], even if a Direction of +1 or -1 is specified! David