Re: Limit Question
- To: mathgroup at smc.vnet.net
- Subject: [mg66465] Re: Limit Question
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Sun, 14 May 2006 02:58:01 -0400 (EDT)
- Organization: The Open University, Milton Keynes, UK
- References: <e43vun$90e$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Blimbaum, Jerry CIV NSWC PC wrote:
> Why do these give no output?
>
> Simplify[Limit[Exp[-a t],t->Infinity],a>0]
>
> and same for
>
> Simplify[Limit[Exp[a t],t->Infinity],a<0]
Hi Jerry,
First, *Simplify* evaluates its arguments. The assumption 'a > 0' is not
passed on to the *Limit* function. Since the limit statement returned
unevaluated -- the result depends on the value of the parameter 'a' and
*Limit* does nothing about 'a' at this stage -- *Simplify* has nothing
to simplify. You can see this process using the *Trace* function (see
In[2]).
To pass the assumption to the limit statement, wrap it inside an
*Assuming* function [1], as in In[3] and In[4].
In[1]:=
Limit[Exp[(-a)*t], t -> Infinity]
Out[1]=
-a t
Limit[E , t -> Infinity]
In[2]:=
Trace[Simplify[Limit[Exp[(-a)*t], t -> Infinity],
a > 0]]
In[3]:=
Assuming[a > 0, Limit[Exp[(-a)*t], t -> Infinity]]
Out[3]=
0
In[4]:=
Assuming[a < 0, Limit[Exp[(-a)*t], t -> Infinity]]
Out[4]=
Infinity
In[5]:=
$Version
Out[5]=
5.2 for Microsoft Windows (June 20, 2005)
Best regards,
Jean-Marc
[1] http://documents.wolfram.com/mathematica/functions/Assuming