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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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