[Date Index]
[Thread Index]
[Author Index]
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:
In[45]:=
limit[f[x,y],x->a]
Out[45]=
Limit[f[x,y],x->a]
In[54]:=
limit[f[x,y],x->a,Analytic->True]
Out[54]=
f[a,y]
while in other cases you ought to get whatever Limit gives (I hope!). Of
course you should not forget about the HoldForm in Out[45] above.
Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/
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[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
>
>
>
>
>
Prev by Date:
**Re: RE: puzzling difference in speed**
Next by Date:
**Re: calculating the azimuth between two lat/lon's**
Previous by thread:
**On Limit[ f[x,y], x->x0 ]**
Next by thread:
**MathML Conference: Final Announcement**
| |