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MathGroup Archive 1999

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RE: Limits of multi-var. functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19924] RE: [mg19795] Limits of multi-var. functions
  • From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
  • Date: Tue, 21 Sep 1999 02:22:54 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Phil Mendelsohn  wrote:
------------------------

I suspect this is an easy question, but I'm not finding it in Help or a
couple of other Mathematica books I have around.

If I want to find the limit of a function of several variables, how do I
do it?  
-----------------------------

You can do either of the following very easiliy:

Limit[Limit[f[x,y],x->x0],y->y0]
Limit[Limit[f[x,y],y->y0],x->x0]

Above you take the limit with respect to one variable while the other
variable is fixed.  However, I am told the following is very difficult.

Limit[f[x,y],{x,y}->{x0,y0}]

Here the problem is weather the limit approaches the same value along all
possible paths towards {x0,y0}.  In general you can approach {x0,y0} from
any direction in the space of complex numbers, but you may want to limit
consideration to real numbers. This is still very difficult if you are only
concerned about real values of (x,y).  One of the lead developers at Wolfram
Research told me there is no known algorithm for this problem.  At least
there was no known algorithm when we had this discussion.  

--------------------
Regards,
Ted Ersek

For Mathematica tips, tricks see 
http://www.dot.net.au/~elisha/ersek/Tricks.html



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