       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 - 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}

Andrzej Kozlowski
Tokyo, Japan

```

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