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