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 > ____________________________________________________________________