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
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
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 -
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