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Re: Limits pre- & post-Solve[]
*To*: mathgroup at smc.vnet.net
*Subject*: [mg14544] Re: Limits pre- & post-Solve[]
*From*: Paul Abbott <paul at physics.uwa.edu.au>
*Date*: Thu, 29 Oct 1998 04:33:37 -0500
*Organization*: University of Western Australia
*References*: <70rkib$4u5$5@dragonfly.wolfram.com>
*Sender*: owner-wri-mathgroup at wolfram.com
Richard W. Klopp (with slight modification) wrote:
> In[1]:= sol = Solve[Integrate[m x + b,{x,0,t+h}]==
> Integrate[n x + c,{x,0,t-h}],h]
>
> Out[1]= {{h -> (-b - c - m*t - n*t -
> Sqrt[b^2 + 2*c*b + 4*n*t*b + c^2 + 4*m*n*t^2 + 4*c*m*t])/
> (m - n)}, {h ->
> (-b - c - m*t - n*t + Sqrt[b^2 + 2*c*b + 4*n*t*b + c^2 +
> 4*m*n*t^2 + 4*c*m*t])/(m - n)}}
>
> However, if I makes the slopes equal before I Solve[], everything's
> fine.
>
> In[2]:= h/.Solve[((Integrate[m x + b,{x,0,t+h}]-Integrate[n x +
> c,{x,0,t-h}])/.n->m)==
> 0,h]
>
> Out[2]= {((-b + c)*t)/(b + c + 2*m*t)}
>
> What's going on and how do I get In[1] to behave as I desire, that is,
> come out with something like Out[2]?
One way is to compute the Series expansion of the pair of solutions
about m == n
In[3]:= (h/.sol)+O[n,m]//Simplify
force the positive square root,
In[4]:= PowerExpand[%]
and then simplify the last solution
In[5]:= %//Last//Normal//Simplify
Out[5]=
(c - b) t
-------------
b + c + 2 m t
Cheers,
Paul
____________________________________________________________________
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia Nedlands WA 6907
mailto:paul at physics.uwa.edu.au AUSTRALIA
http://www.physics.uwa.edu.au/~paul
God IS a weakly left-handed dice player
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