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 > > > > >