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 ____________________________________________________________________