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.