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

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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