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 - λ/μ. Mathematica can deal with all > three possible cases (it is also pretty obvious when done by hand): > > (Limit[(1 - E^((-μ)*t* > (s - 1 - λ/μ)))/ > (s - 1 - λ/μ), > t -> Infinity, > Assumptions -> > {μ > 0 && #1[s, > 1 + λ/μ]}] & ) /@ > {Greater, Equal, Less} > > {-(μ/(λ - s*μ + μ)), > 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
- References:
- Limit of an expression?
- From: Virgil Stokes <vs@it.uu.se>
- Limit of an expression?