limit multivariable functions

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b.baillette - 08 Oct 2008 19:27 GMT

Hello,

Is it possible to evaluate, with Maple, the limit of a multivariable
function ?

For instance, let the mapping :

f : R² --> R, with : f(x) = xy²/(x² + y) if x \neq 0 and f(x) = 0 if x =0.

We have, of course, \lim_{(x,y) \to (0,0)} f(x,y) = 0.

I would like to know if there is a Maple command with which I could evaluate
this limit.

Thanks in advance for your responses,

Bruno.

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John Harper - 09 Oct 2008 00:13 GMT

>Hello,
>
[quoted text clipped - 6 lines]
>
>We have, of course, \lim_{(x,y) \to (0,0)} f(x,y) = 0.

But with some things rather like that there is real trouble, e.g. if
g(x,y) = x*y/(x^2+y^2), \lim_{x \to 0}(\lim_{y \to 0} g(x,y)) = 0, but
lim_{x \to 0} g(x,x) = 1/2 so no unique limit as (x,y) to (0,0) exists.

-- John Harper, School of Mathematics, Statistics and Computer Science,
Victoria University, PO Box 600, Wellington 6140, New Zealand
e-mail john.harper@vuw.ac.nz phone (+64)(4)463 6780 fax (+64)(4)463 5045

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Thomas Richard - 09 Oct 2008 08:22 GMT

> Is it possible to evaluate, with Maple, the limit of a multivariable
> function ?

Yes, please see ?limit,multi (that page is linked from the ?limit
page).

--
Thomas Richard
Technical Support Maple/MapleSim
Scientific Computers GmbH
http://www.scientific.de

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Mate - 09 Oct 2008 20:36 GMT

> > Is it possible to evaluate, with Maple, the limit of a multivariable
> > function ?
[quoted text clipped - 6 lines]
> Technical Support Maple/MapleSim
> Scientific Computers GmbHhttp://www.scientific.de

But you must admit that Maple is very weak here.
Simple limits like

limit(x^2*y/(x^2+y^2), {x=0,y=0});

are beyond its capability.

Mate

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Math Forum / Math Software / Maple / October 2008

limit multivariable functions