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Re: Beginner question: operating on piecewise defined functions

• To: mathgroup at smc.vnet.net
• Subject: [mg41698] Re: [mg41609] Beginner question: operating on piecewise defined functions
• From: "German Buitrago A." <gerbual at col2.telecom.com.co>
• Date: Sat, 31 May 2003 06:07:46 -0400 (EDT)
• References: <200305280857.EAA09573@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

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
Subject: [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.
>

• References:
  • Beginner question: operating on piecewise defined functions
    • From: Jan Rychter <jan@rychter.com>