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Failures (?) in Limit[f[x,y],x->x0]

• To: mathgroup at smc.vnet.net
• Subject: [mg34720] Failures (?) in Limit[f[x,y],x->x0]
• From: Jack Goldberg <jackgold at umich.edu>
• Date: Mon, 3 Jun 2002 01:46:38 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hi Group,

Consider this for starters:

(1)    	Limit[ f[x], x->0 ]  returns unmodified

as it should.

(2)  	Limit[ f[x], x->0, Analytic->True ] returns  f[0].

This is what the
help menu says should happen and it does.

Now,

(3)	Limit[ f[x,y],  x->0 ]  returns  f[0,y]  !!!!!

This is bad news for many reasons besides the obvious violation of the
definition as given in the Help.  It may be wrong if  f[x,y]  is
discontinuous at  x = 0.  By the way, you can replace  0  by any parameter
and write f as any function with 2 or more variables WHICH IS NOT
built-in.  I have not checked it using built-in functions of more than one
variable.

I hope I am missing something because my work requires that Limit obey the
rules I thought I understood by readin  ? Limit .  As always, I am
grateful for your thoughts and comments.

Jack