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Re: Tough Limit

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92714] Re: Tough Limit
  • From: carlos at colorado.edu
  • Date: Sat, 11 Oct 2008 06:44:20 -0400 (EDT)
  • References: <gckmsj$nh8$1@smc.vnet.net> <gcn46h$71e$1@smc.vnet.net>

On Oct 10, 2:36 am, Peter Pein <pet... at dordos.net> wrote:
> car... 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.

Correct.  The limit comes from a Laplace Transform homework exercise
for sophomores. Mathematica was allowed, along with three other CAS.
Students check their solution with tables.


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