Re: Limit of an expression?
- To: mathgroup at smc.vnet.net
- Subject: [mg67520] Re: [mg67479] Limit of an expression?
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Thu, 29 Jun 2006 00:09:54 -0400 (EDT)
- References: <200606280751.DAA03399@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
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} Andrzej Kozlowski Tokyo, Japan
- References:
- Limit of an expression?
- From: Virgil Stokes <vs@it.uu.se>
- Limit of an expression?