Services & Resources / Wolfram Forums
MathGroup Archive
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1999

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Limits of multi-var. functions

  • To: mathgroup at
  • Subject: [mg19860] Re: [mg19795] Limits of multi-var. functions
  • From: "David Park" <djmp at>
  • Date: Sun, 19 Sep 1999 01:20:43 -0400
  • Sender: owner-wri-mathgroup at


You have to take two limits in succession, or by following some path in the xy-plane.
If you get different answers depending upon the order or path, then the limit does
not really exist. Keeping this in mind, here is one method:

Fold[Limit[#1, #2] &, x^2 y^2 - 2x y^5 + 3y, {{x -> 2}, {y -> 3}}]

Fold[Limit[#1, #2] &, x^2 y^2 - 2x y^5 + 3y, {{y -> 3}, {x -> 2}}]

Here is a second method which approaches along a specific line in the xy-plane.

f[x_, y_] := x^2 y^2 - 2x y^5 + 3y
Limit[f[x, 3/2x], {x -> 2}]

David Park
djmp at

>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}]
>for example, but this gave me two results; one case if x approaches 2
>(leaving y unevaluated) and the other case if y approaches 3 (leaving x
>unevaluated.)  I'd like to evaluate for both simultaneously.
>Did I miss something -- I do know that convergence of the limit is
>proportionally more complex in several vars, but expected that Mathematica would
>do it.  (Running Mathematica v3.0.1, Linux)
>Thanks -- Phil Mendelsohn

  • Prev by Date: Re: F[f_,x_]:=f[x] ?
  • Previous by thread: Re: Limits of multi-var. functions
  • Next by thread: Re: Limits of multi-var. functions