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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