Re: Problem with Limit
- To: mathgroup at smc.vnet.net
- Subject: [mg66864] Re: Problem with Limit
- From: "Scout" <Scout at nodomain.com>
- Date: Fri, 2 Jun 2006 04:08:24 -0400 (EDT)
- References: <e5jri2$dos$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
"Tony Harker" <a.harker at ucl.ac.uk> news:e5jri2$dos$1 at smc.vnet.net... > > 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 > > Could it be a bug of Limit[] command? However the 0 value of the limit is incorrect. Limit[] therefore makes no explicit assumptions about functions, so the square roots can be the arising problem, specially with more symbols (k,g,m1,m2). Assuming[] doesn't improve it, in fact: In[1]:= Assuming[k > 0 && m1 > 0 && m2 > 0, Limit[t, g -> 0]] Out[1]= 0 In[2]:= $Version Out[2]= "5.2 for Microsoft Windows (June 20, 2005)" But, In[3]:= v = Limit[Simplify[Together[t]], g->0] Out[3]= \!\(\(\(1\/\(2\ k\ \((m1 - m2)\)\)\)\((\@\(k\^2\ \((m1 - m2)\)\^2\)\ \((\(-\@\(\(\(-\@\(k\^2\ \ \((m1 - m2)\)\^2\)\) + k\ \((m1 + m2)\)\)\/\(m1\ m2\)\)\) + \@\(\(\@\(k\^2\ \ \((m1 - m2)\)\^2\) + k\ \((m1 + m2)\)\)\/\(m1\ m2\)\))\) + k\ \((m1 - m2)\)\ \((\@\(\(\(-\@\(k\^2\ \((m1 - m2)\)\^2\)\) + k\ \((m1 + \ m2)\)\)\/\(m1\ m2\)\) + \@\(\(\@\(k\^2\ \((m1 - m2)\)\^2\) + k\ \((m1 + m2)\)\ \)\/\(m1\ m2\)\))\))\)\)\) In[4]:= Simplify[v, {m1 > m2 && k > 0}] Out[4]= \!\(\@2\ \@\(k\/m2\)\) Regards, ~Scout~