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MathGroup Archive 2006

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Re: Limit of an expression?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67517] Re: Limit of an expression?
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Thu, 29 Jun 2006 00:09:49 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 6/28/06 at 3:51 AM, vs at it.uu.se (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]\)\)

You have not provided enough information to answer the question.

Look at just the exponential (the only part of the expression that is a function of t). The exponent is -u t (s - 1 - y/u)

If s > y/u+1, the limit will exist for u>0 and be 0. But if this is not the case, the expression will have no limit
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