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

```

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