RE: Re: Several variab

*To*: mathgroup at smc.vnet.net*Subject*: [mg8533] RE: [mg8409] Re: [mg8340] Several variab*From*: Ersek_Ted%PAX1A at mr.nawcad.navy.mil*Date*: Thu, 4 Sep 1997 02:20:40 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Nacho wrote: > > It is possible to do several variable limits in Mathematica 3.0? > Jens replied: | | Limit[Limit[x^2+y^2,x->0],y->0] | | works. But keep in mind that the order of limit's is *not* arbitarry! | The method above will often fail to identify cases where the Limit does not exist. However, I think the above will work where the function is continuous. Consider the following example: In[1]:= f[x_, y_]:= x y/(2 x^2 + y^2) In[2]:= Limit [ Limit [ f[x,y], x->0 ], y->0 ] Out[2]= 0 In[3]:= Limit [ Limit [ f[x,y], y->0 ], x->0 ] Out[3]= 0 Both of the above suggest the Limit is zero. However, ............ In[4]:= Limit[ f[x,y]/. x-> y/2, y->0] Out[4]= 1/3 In[5]:= Limit[ f[x,y]/. x-> y/3, y->0] Out[5]= 3/11 Since the result depends on how {x,y} are related as they approach {0,0} we say the Limit does not exist. The other day I sent in a different approach that as far as I can tell will give the right answer for any problem it can handle. For the example above my approach gives Indeterminate. Ted