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Re: Problem with Limit

• To: mathgroup at smc.vnet.net
• Subject: [mg66833] Re: [mg66805] Problem with Limit
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 1 Jun 2006 06:54:25 -0400 (EDT)
• References: <200605311030.GAA13862@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On 31 May 2006, at 19:30, Tony Harker 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.
>
>
> Dr A.H. Harker
> Department of Physics and Astronomy
> University College London
> Gower Street
> London
> WC1E 6BT
>
>


Mathematica 5.1 gives 0 in all of the above cases. Moreover:

In[48]:=
t + O[g]^1

Out[48]=
O[g]^1

which agrees with it.

Andrzej Kozlowski
Tokyo, Japan