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Re: Tough Limit

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92687] Re: Tough Limit
  • From: Szabolcs Horvát <szhorvat at gmail.com>
  • Date: Fri, 10 Oct 2008 04:36:39 -0400 (EDT)
  • Organization: University of Bergen
  • 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)  ?
> 

You have to tell the assumptions to Limit too:

Limit[Integrate[Sin[\[Omega] t] E^(-s t), {t, 0, x},
   Assumptions -> s > 0], x -> \[Infinity],
  Assumptions -> s > 0 && \[Omega] \[Element] Reals]

To make things simpler and avoid duplication we could use Assuming:

Assuming[s > 0 && \[Omega] \[Element] Reals,
  Limit[Integrate[Sin[\[Omega] t] E^(-s t), {t, 0, x}],
   x -> \[Infinity]]]


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