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