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Re: Tough Limit

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92673] Re: Tough Limit
  • From: Peter Pein <petsie at dordos.net>
  • Date: Fri, 10 Oct 2008 04:34:07 -0400 (EDT)
  • References: <gckmsj$nh8$1@smc.vnet.net>

carlos at colorado.edu schrieb:
> 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)  ?
> 

Keeping in mind that
Integrate[f[x],{x,x0,Infinity}] is by def.
Limit[Integrate[f[x],{x,x0,x1},x1->Infinity],

Integrate[Sin[\[Omega]*t]*Exp[-s*t],{t,0,Infinity},Assumptions -> s>0]
or
LaplaceTransform[Sin[\[Omega]*t],t,s]

should (don't have Mathematica installed on this system) give the desired result.


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