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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~