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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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