Re: Limit of an expression?
- To: mathgroup at smc.vnet.net
- Subject: [mg67515] Re: Limit of an expression?
- From: "Scout" <Scout at nodomain.com>
- Date: Thu, 29 Jun 2006 00:09:35 -0400 (EDT)
- References: <e7td7i$3lg$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
"Virgil Stokes" <vs at it.uu.se> news:e7td7i$3lg$1 at smc.vnet.net... > 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 > Hi, you could assume that (s-1-Lambda/Mu)>0: In[1]:= \!\(Assuming[\[Mu] > 0\ && \ \((s - 1 - \[Lambda]/\[Mu])\) > 0, Limit[\(1 - \[ExponentialE]\^\(\(-\[Mu]\)\ t\ \((s - 1 - \ \[Lambda]\/\[Mu])\)\)\)\/\(s - 1 - \[Lambda]\/\[Mu]\), t \[Rule] \[Infinity]]]\) Out[1]= \!\(\(-\(\[Mu]\/\(\[Lambda] + \[Mu] - s\ \[Mu]\)\)\)\) HTH, ~Scout~