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MathGroup Archive 1998

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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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