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Re: Tough Limit

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92668] Re: Tough Limit
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Fri, 10 Oct 2008 04:33:12 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <gckmsj$nh8$1@smc.vnet.net>

carlos at colorado.edu wrote:

> How can I get
> 
> 
> Limit[Integrate[Sin[\[Omega]*t]*Exp[-s*t],{t,0,x},
>       Assumptions->s>0],x->\[Infinity]]
> 
> to answer \[Omega]/(\[Omega]^2+s^2)  ?

Perhaps by telling Mathematica that omega is real... since Mathematica 
works over the field of complex numbers, by default.

In[9]:= Assuming[s > 0 && Im[\[Omega]] == 0,
  Limit[Integrate[Sin[\[Omega]*t]*Exp[-s*t], {t, 0, x}],
   x -> \[Infinity]]]

Out[9]= \[Omega]/(s^2 + \[Omega]^2)

Regards,
-- Jean-Marc


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