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

• To: mathgroup at smc.vnet.net
• Subject: [mg34780] On Limit[ f[x,y], x->x0 ]
• From: Jack Goldberg <jackgold at umich.edu>
• Date: Thu, 6 Jun 2002 01:55:05 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hi Group,

If this is a repeat please forgive.  I have not seen my original post.

There appears to be some unfortunate behavior of  Limit[f[x,y],x->x0].

Limit[ f[x], x->0 ]  for general f  simply returns the limit unevaluated
unless the option  Analytic->True is invoked and then

	Limit[ f[x], x->0 ]  returns  f[0]

However, if f  is a function of more that 1 variable or has more than 1
slot, we get this unexpected behavior:

	Limit[ f[x,y,1], x->0 ]  returns f[0,x,1]

whether or not the option  Analytic->True is invoked.  Likewise for the
functions   f[x,x],  f[x,y], f[x,y,z] etc.  Of course  x->0 is not the
essential feature,  x->x0  results in the same "errors".

I hate to call this a bug, but it sure 'taint a feature!  After all, if  f
is discontinuous at  x0,  the expression returned could be (and often is)
false.  A second difficulty with this "feature" is that the conditional

	/; "some expression involving Limit"

will evaluated when such evaluation is not expected.

Comments appreciated!  As usual -

Jack