Re: Is this normal for Limit?

• To: mathgroup at smc.vnet.net
• Subject: [mg82294] Re: Is this normal for Limit?
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Wed, 17 Oct 2007 03:58:05 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <ff1par\$8nq\$1@smc.vnet.net>

```Michael Mandelberg wrote:
> I have what I would think is the following simple limit to evaluate:
>
> \$Pre = Refine[#] &;
> \$Assumptions = {t \[Element] Reals, k \[Element] Reals,  k > 0};
>
> In[3]:= Limit[Exp[-k t], t -> Infinity]
>
> The results is:
>
> Out[3]= Limit[\[ExponentialE]^(-k t), t -> \[Infinity]]
>
> In other words Mathematica 6.0.0 punts on this.  Is there any sense in
> which this limit is not well-defined?

It is very well-defined, indeed, though I am clueless about what is
going on on your system. Note that you only need k positive as
assumption and Refine is useless (in this case) since Limit already uses
whatever is defined in \$Assumptions.

In[1]:= Limit[Exp[-k t], t -> Infinity, Assumptions -> k > 0]

Out[1]= 0

In[2]:= Block[{\$Assumptions = k > 0}, Limit[Exp[-k t], t -> Infinity]]

Out[2]= 0

In[3]:= \$Assumptions = k > 0;

In[4]:= Limit[Exp[-k t], t -> Infinity]

Out[4]= 0

In[5]:= Refine[Limit[Exp[-k t], t -> Infinity]]

Out[5]= 0

In[6]:= \$Version

Out[6]= "6.0 for Microsoft Windows (32-bit) (June 19, 2007)"

Regards,
--
Jean-Marc

```

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