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]]]