Re: Limits of multi-var. functions

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

Phil, 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}}] {-927} Fold[Limit[#1, #2] &, x^2 y^2 - 2x y^5 + 3y, {{y -> 3}, {x -> 2}}] {-927} 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}] {-927} David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ >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 > >