RE: Several variables limit?
- To: mathgroup at smc.vnet.net
- Subject: [mg8413] RE: [mg8340] Several variables limit?
- From: Ersek_Ted%PAX1A at mr.nawcad.navy.mil
- Date: Sat, 30 Aug 1997 00:42:19 -0400
- Sender: owner-wri-mathgroup at wolfram.com
Nacho wrote:
|
| It is possible to do several variables limits in Mathematica 3.0?
|
This capability isn't built in, but I think I found a way to write the code
for it.
Strange, but I couldn't find a way to make this a DownValue for Limit.
So I made my own function "Lim".
In[1]:= Lim[expr_, {x_->x0_, y_->y0_}]/;
(Abs[x0]<Infinity && Abs[y0]<Infinity):=
Module[{a, z, cx, cy},(
a=Limit[expr/.{x->x0+cx*eps, y->y0+cy*eps}, eps->0];
If[ FreeQ[a,cx]&&FreeQ[a,cy],a, Indeterminate]
)]
My code gives the right answer for the following non-trivial problems
out of a text book.
In[2]:= Lim[(x^2 - y^2)/(x-y), {x->0, y->0}]
Out[2]= 0
In[3]:= Lim[x y/ (x^2+y^2), {x->0, y->0}]
Out[3]:= Indeterminate
If you invest enough effort you can generalize this to a Limit in
n-dimensions, and allow for a user specified Direction.
A few weeks ago I sent this to WRI, and asked them to include it in
future versions of Mma. Maybe they will include it.
Ted Ersek