Re: On Limit[ f[x,y], x->x0 ]
- To: mathgroup at smc.vnet.net
- Subject: [mg34792] Re: [mg34780] On Limit[ f[x,y], x->x0 ]
- From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
- Date: Fri, 7 Jun 2002 01:08:54 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I agree that it looks like a possible oversight. The only thing I can
suggest is something like this:
limit[f_[x_], Rule[a_, b_], opts___] := Limit[f[x], Rule[a, b], opts];
limit[f_[x__], Rule[a_, b_], opts___] /;
MemberQ[Attributes[f], NumericFunction] :=
Limit[f[x], Rule[a, b], opts];
limit[f_[x__], Rule[a_, b_], opts___, Analytic -> True, opts1___] :=
Limit[f[x], Rule[a, b], opts, Analytic -> True, opts1];
limit[f_[x__], Rule[a_, b_], opts___] :=
HoldForm[Limit[f[x], Rule[a, b], opts]]
Now you get:
while in other cases you ought to get whatever Limit gives (I hope!). Of
course you should not forget about the HoldForm in Out above.
Toyama International University
On Thursday, June 6, 2002, at 02:55 PM, Jack Goldberg wrote:
> 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
> 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
> 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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