Re: Tough Limit
- To: mathgroup at smc.vnet.net
- Subject: [mg92671] Re: Tough Limit
- From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
- Date: Fri, 10 Oct 2008 04:33:45 -0400 (EDT)
- 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) ?
In[2]:= Assuming[s > 0 && Element[\[Omega], Reals],
Limit[Integrate[Sin[\[Omega]*t]*Exp[(-s)*t], {t, 0, x}], x -> Infinity]]
Out[2]= \[Omega]/(s^2 + \[Omega]^2)
David