Re: Double limits at the infinity.
- From: David C. Ullrich <ullrich@xxxxxxxxxxxxxxxx>
- Date: Thu, 21 Jul 2005 08:29:34 -0500
On Thu, 21 Jul 2005 13:46:25 +0200, Jesús Cid-Sueiro
<jcid@xxxxxxxxxxx> wrote:
>Given function f(x,y) I would need to know under which conditions over
>f, the limit of f as x,y go to +infinity does not depend on the way to
>go, for instance
>
>lim_{y-->inf} lim_{x-->inf) f(x,y) =
>lim_{x-->inf) lim_{y-->inf} f(x,y) =
>lim_{x-->inf} f(x,x) =
>
>
>I guess that the above relations are true if the limit exists, f is
>continuous and df(x,y)/dx and df/dy always go to zero as x and y go to
>+inf (in any way).
>
>Is this correct?
I'm not sure what you mean by "the limit exists".
Of course if you mean "if lim_{(x,y) -> (inf,inf)} f(x,y)
exists then the answer is yes, all the above are equal.
But that's probably not what you mean, since that's
pretty obvious, and also has nothing to do with the
conditions on the derivatives.
If you mean
">I guess that the above relations are true if
lim_{y-->inf} lim_{x-->inf) f(x,y) exists, f is continuous
and df(x,y)/dx and df/dy always go to zero as x and y go to
+inf (in any way)"
then the answer is no.
>Jesús.
************************
David C. Ullrich
.
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