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MathGroup Archive 1995

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why can't mma find this limit ??

  • To: mathgroup at smc.vnet.net
  • Subject: [mg2418] why can't mma find this limit ??
  • From: Christian.Jost at epc.u-psud.fr (Christian Jost)
  • Date: Sun, 5 Nov 1995 16:05:37 -0500
  • Organization: Universite Paris-Sud XI

I have the simple function

n[t_]=3DK n0/((K-n0) Exp[-r t] + n0) (the solution of logistic growth
                                    dN/dt=3Dr (1-N/K) N )

In the limit t=3D0 this function is n0 and mma can calculate this. The li=
mit
for Inifinity is obviously K, but mathematica returns the limit
unevaluated
In:
  Limit[n[t],t->Infinity]
Out:
  Limit[(K*n0)/((K - n0)/E^(r*t) + n0),=20
=20
  t -> DirectedInfinity[1]]

Any idea why? Is there a package that helps for such problems?

Thanks, Christian.

--=20
Christian Jost, Universit=E9 Paris-Sud XI, Orsay, France
jost at psisun.u-psud.fr


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