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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: [mg39349] RE: [mg39333] Limits: Is there something I'm missing Here?
  • From: "David Park" <djmp at earthlink.net>
  • Date: Wed, 12 Feb 2003 03:52:30 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

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





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