Re: Limit of an expression?
- To: mathgroup at smc.vnet.net
- Subject: [mg67601] Re: Limit of an expression?
- From: "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com>
- Date: Sat, 1 Jul 2006 05:13:17 -0400 (EDT)
- References: <200606280751.DAA03399@smc.vnet.net><e7vkut$smg$1@smc.vnet.net> <e82omj$rau$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
On 6/30/06, Virgil Stokes <vs at it.uu.se> wrote:
> s=.;
> (Limit[E^(-μ*t)*(1-E^(-μ*t*(s-1-λ/μ)))/(s-1-λ/μ),t -> Infinity,
> Assumptions -> {μ > 0 && s > 0 && λ/(s*μ) < 1 && #1[s,1 + λ/μ]}] & ) /@
> {Greater, Equal, Less}
>
> I believe that this is ok for the new problem.
> What do you get?
Hi Virgil,
Here is what I get,
In[2]:=
(Limit[(1 - E^((-mu)*t*(s - 1 - lambda/mu)))/
(s - 1 - lambda/mu)/E^(mu*t), t -> Infinity,
Assumptions -> {mu > 0 && s > 0 &&
lambda/(s*mu) < 1 && #1[s,
1 + lambda/mu]}] & ) /@ {Greater, Equal, Less}
Out[2]=
{0, 0, 0}
However, I wonder how Mathematica was able to compute a value for the
second limit since the function is not defined if s == 1 + lambda / mu
(the denominator is null).
Regards,
Jean-Marc
P.S. I must thanks David W. Cantrell for having pointed out this issue
that was already present in my answer to your previous question about
limits. See
http://groups.google.com/gr
oup/comp.soft-sys.math.mathematica/browse_thread/thread/ca73244620e68406/e08485378e1c311c?q=L
imit+of+an+expression%3F+David+W.Cantrell+&rnum=1#e08485378e1c311c