RE: Several variables limit?

• To: mathgroup at smc.vnet.net
• Subject: [mg8413] RE: [mg8340] Several variables limit?
• 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

```