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MathGroup Archive 1999

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Re: Limits of multi-var. functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19897] Re: Limits of multi-var. functions
  • From: "Kai G. Gauer" <gauer at sk.sympatico.ca>
  • Date: Sun, 19 Sep 1999 18:47:42 -0400
  • References: <7rsh34$3gf@smc.vnet.net> <7s1o5r$9l6@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com


Paul Abbott wrote:

> Phil Mendelsohn wrote:
>
> > I suspect this is an easy question, but I'm not finding it in Help or a
> > couple of other Mathematica books I have around.
> >
> > If I want to find the limit of a function of several variables, how do I
> > do it?  In the case of a polynomial function, I tried
> >
> > Limit[x^2 y^2 - 2x y^5 + 3y, {x->2, y->3}]
>
> The syntax you want is
>
>     Limit[Limit[x^2*y^2 + 3*y - 2*x*y^5, x -> 2], y -> 3]
>
> or
>
>     Limit[Limit[x^2*y^2 + 3*y - 2*x*y^5, y -> 3], x -> 2]
>
> both of which give you the same result.
>

Ok, but any student of mathematics would obviously know that it is NOT always
necessarily the case that:

    lim[lim[f(x,y)]] <> lim[lim[f(x,y)]] <> lim [f(x,y)]
    x=a y=b               y=b x=a               (x,y)=(a,b)

Can anyone modify Limit for multiple variables to do the right thing and
differentiate when to use which version of limit?

By the way, I can think of a lot of functions in which the first two equations
are the same, but by choosing another (aritrary) "path" to (a,b) gives an
answer of undefined/no limit.

> Cheers,
>     Paul
>
> --
> ____________________________________________________________________
> Paul Abbott                                   Phone: +61-8-9380-2734
> Department of Physics                           Fax: +61-8-9380-1014
> The University of Western Australia
> Nedlands WA  6907                     mailto:paul at physics.uwa.edu.au
> AUSTRALIA                            http://physics.uwa.edu.au/~paul
>
>             God IS a weakly left-handed dice player
> ____________________________________________________________________





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