Re: Problem with Limit
- To: mathgroup at smc.vnet.net
- Subject: [mg66832] Re: Problem with Limit
- From: "David W.Cantrell" <DWCantrell at sigmaxi.org>
- Date: Thu, 1 Jun 2006 06:54:23 -0400 (EDT)
- References: <e5jri2$dos$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
"Tony Harker" <a.harker at ucl.ac.uk> wrote: > Can anybody explain why, for > > t =Sqrt[(k*m1 + k*m2 + m1*g + m2*g - > (1/2)*Sqrt[4*(m1 + m2)^2*(k + g)^2 - 16*k*m1*m2*(k + 2*g)])/ > (m1*m2)]/(1 + (k*m1 - k*m2 + m1*g - m2*g + > (1/2)*Sqrt[4*(m1 + m2)^2*(k + g)^2 - 16*k*m1*m2*(k + 2*g)])^2/ > (4*m1*m2*g^2)) + Sqrt[(k*m1 + k*m2 + m1*g + m2*g + > (1/2)*Sqrt[4*(m1 + m2)^2*(k + g)^2 - 16*k*m1*m2*(k + 2*g)])/ > (m1*m2)]/(1 + ((-k)*m1 + k*m2 - m1*g + m2*g + > (1/2)*Sqrt[4*(m1 + m2)^2*(k + g)^2 - 16*k*m1*m2*(k + 2*g)])^2/ > (4*m1*m2*g^2)); > > Limit[t, g -> 0] > Limit[Together[t], g -> 0] > > both give zero, whereas > > Limit[Simplify[Together[t]], g -> 0] > > gives a non-zero result? This is with Mathe4matica 5.2. Interesting question. I haven't looked at it carefully enough to be able to explain why. But, FWIW, I certainly think the nonzero result is the correct one. With the assumptions that m1 and m2 are real and that k > 0, that simplifies to Sqrt[2*k/m2] At first, that surprised me because I had thought, based on just a quick glance, that t was symmetric wrt m1 and m2. But it's not, I see now. David