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MathGroup Archive 1997

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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: 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



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