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MathGroup Archive 2003

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Re: Limits: Is there something I'm missing Here?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39348] Re: Limits: Is there something I'm missing Here?
  • From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
  • Date: Wed, 12 Feb 2003 03:52:21 -0500 (EST)
  • References: <b2ahti$pl4$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"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


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