Re: Re: Beginner question: operating on piecewise defined functions
- To: mathgroup at smc.vnet.net
- Subject: [mg41706] Re: [mg41698] Re: [mg41609] Beginner question: operating on piecewise defined functions
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Mon, 2 Jun 2003 04:35:16 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Actually is is just by accident that the Limit package works in this case. In fact, it will only work in cases when Limit[f[x],x ->a] is actually equal to f[a]. So the following fails: In[1]:= << "Calculus`Limit`" In[2]:= f[x_] := 1/x^2 /; x >= 1 In[3]:= f[x_] := Sin[x]/x /; x < 1 In[4]:= Limit[f[x], x -> 0] Out[4]= Limit[f[x], x -> 0] Andrzej Kozlowski Yokohama, Japan http://www.mimuw.edu.pl/~akoz/ http://platon.c.u-tokyo.ac.jp/andrzej/ On Saturday, May 31, 2003, at 07:07 pm, German Buitrago A. wrote: > Jan, > > you can use the Standard Add-On Package Calculus`Limit` and you should > keep > in mind the syntax of the function Limit: > > ?Limit > > "Limit[expr, x->x0] finds the limiting value of expr when x approaches > x0." > > (Appreciate that the couple {} is not required around of "x -> > Infinity") > > In[1]:= > f[x_] := 1/x^2 /; x >= 1 > > In[2]:= > f[x_] := 1 /; x < 1 > > In[5]:= > << Calculus`Limit` > > In[6]:= > Limit[f[x], x -> Infinity] > > Out[6]= > 0 > > Greetings, > > German Buitrago A. > Manizales, Colombia > > > > ----- Original Message ----- > From: "Jan Rychter" <jan at rychter.com> To: mathgroup at smc.vnet.net > To: mathgroup at smc.vnet.net > Subject: [mg41706] [mg41698] [mg41609] Beginner question: operating on piecewise > defined > functions > > >> If I define a piecewise function as, say: >> >> f[x_] := 1/x^2 /; x >= 1 >> f[x_] := 1 /; x < 1 >> >> then how can I get Mathematica to operate on it, as in: >> >> Limit[f[x], {x->Infinity}] >> >> Just trying that returns the expression unevaluated, even though >> defining: >> >> g[x_] := 1/x^2 >> >> and trying: >> Limit[g[x], {x -> Infinity}] >> >> Yields, as expected: >> >> Out[7]= >> {0} >> >> thanks, >> --J. >> > > >