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Re: Limit of an expression?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg67557] Re: Limit of an expression?
*From*: "David W.Cantrell" <DWCantrell at sigmaxi.org>
*Date*: Fri, 30 Jun 2006 04:15:25 -0400 (EDT)
*References*: <200606280751.DAA03399@smc.vnet.net> <e7vkut$smg$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote:
> On 28 Jun 2006, at 16:51, Virgil Stokes wrote:
>
> > In the following expression, s is an integer (>= 1), Lambda, Mu, and t
> > are real numbers and all > 0.
> > What is the limit of the following as t goes to infinity?
> >
> > \!\(\(1 - \[ExponentialE]\^\(\(-\[Mu]\)\ t\ \((s - 1 - \
> > \[Lambda]\/\[Mu])\)\)\)\/\(s - 1 - \[Lambda]\/\[Mu]\)\)
> >
> > --V. Stokes
> >
>
> Unless you made a mistake in the formula you posted, the answer
> depends on the sign of s - 1 - Î»/Î¼. Mathematica can deal with all
> three possible cases (it is also pretty obvious when done by hand):
>
> (Limit[(1 - E^((-Î¼)*t*
> (s - 1 - Î»/Î¼)))/
> (s - 1 - Î»/Î¼),
> t -> Infinity,
> Assumptions ->
> {Î¼ > 0 && #1[s,
> 1 + Î»/Î¼]}] & ) /@
> {Greater, Equal, Less}
>
> {-(Î¼/(Î» - s*Î¼ + Î¼)),
> 0, Infinity}
Much of the above is illegible to me, but I'm guessing that the middle case
is equivalent to
In[1]:= Assuming[a==0, Limit[(1 - Exp[a t])/a, t->Infinity]]
Out[1]= 0
which does not seem to be reasonable in Mathematica. I would have expected
Indeterminate instead.
David
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