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