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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: ownerwrimathgroup 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
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