Re: Tough Limit
- To: mathgroup at smc.vnet.net
- Subject: [mg92661] Re: [mg92644] Tough Limit
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Fri, 10 Oct 2008 04:31:56 -0400 (EDT)
- References: <200810091036.GAA24087@smc.vnet.net>
On 9 Oct 2008, at 19:36, 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) ? > First, the answer you give is not correct without the assumption that Omega is real. For example, take Omega = 2Pi I and take s= 2Pi and you will easily see that the integral does not converge. So assuming that Omega is real you get: FullSimplify[Limit[ Integrate[Sin[\[Omega]*t]/ E^(s*t), {t, 0, x}], x -> Infinity, Assumptions -> s > 0 && Im[\[Omega]] == 0], Assumptions -> s > 0 && Element[\[Omega], Reals]] \[Omega]/(s^2 + \[Omega]^2) or, more simply: Integrate[Sin[\[Omega]*t]/E^(s*t), {t, 0, Infinity}, Assumptions -> s > 0 && Im[\[Omega]] == 0] \[Omega]/(s^2 + \[Omega]^2) Andrzej Kozlowski
- References:
- Tough Limit
- From: carlos@colorado.edu
- Tough Limit