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[MUG] Limit Superior & Limit Inferior
| [MUG] Limit Superior & Limit Inferior |
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Author: Classen, Manfred
Posted: Sat, 9 Nov 2002 18:29:33 +0100
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>> From: "Classen, Manfred" "m.classen"
Dear Maple Experts
I would like to know, if there is a Maple command for building the Limit
Superior or Limit Inferior
respectivly. In case there is one, please, tell me in which package it is
included. If there isn't
such a command in the ordinary Maple programm, could you tell me, if there
is any such package
available in the internet? (What is the adress of such an internet page?)
Thanks for your help in advance.
Manfred
Manfred Classen
Rechenzentrum der RWTH-Aachen
Seffenter Weg 23
D-52070 Aachen
Germany
"m.classen"
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| [MUG] Re: Limit Superior & Limit Inferior |
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Author: Maple User Group
Posted: Fri, 15 Nov 2002 10:50:07 -0500
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>> From: Maple User Group "maple_gr"
-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-
Date: Mon, 11 Nov 2002 16:57:14 -0800 (PST)
From: Robert Israel "israel"
To: "maple-list"
Subject: Limit Superior & Limit Inferior
In some cases, "limit" returns a range and you can take the left or
right endpoint. For example:
> limit(sin(x), x=infinity);
-1 .. 1
So you could design a rather crude "limsup" as
> limsup:= proc()
local r;
r:= limit(args);
if type(r,range) then rhs(r)
else r
fi
end;
But it will not be very powerful, because in many cases limit just returns
undefined even though there may be a lim sup.
Robert Israel "israel"
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
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Date: Thu, 14 Nov 2002 07:05:35 -0500 (EST)
From: Carl Devore "devore"
To: "maple-list"
Subject: Limit Superior & Limit Inferior
Maple's ordinary limit command sometimes returns results as a range. For
example,
limit((-1)^n, n= infinity);
-1..1
The documentation does not claim that these numbers are the LimInf and
LimSup, but I do not know of a case where they are not.
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| [MUG] Re: Limit Superior & Limit Inferior |
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Author: Robert Israel
Posted: Mon, 18 Nov 2002 13:04:36 -0800
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>> From: Robert Israel "israel"
Carl Devore "devore" wrote:
> Maple's ordinary limit command sometimes returns results as a range. For
> example,
> limit((-1)^n, n= infinity);
> -1..1
>
> The documentation does not claim that these numbers are the LimInf and
> LimSup, but I do not know of a case where they are not.
Here's one:
> limit(sin(x)-sin(x)^2, x=infinity);
-2 .. 1
The actual lim sup is 1/4.
Robert Israel "israel"
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
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| [MUG] Re: Limit Superior & Limit Inferior |
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Author: Barsuhn
Posted: Tue, 26 Nov 2002 18:22:42 +0100
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>> From: Barsuhn "barsuhn"
> >> From: Robert Israel "israel"
>
> Carl Devore "devore" wrote:
>
> > Maple's ordinary limit command sometimes returns results as a range. For
> > example,
> > limit((-1)^n, n= infinity);
> > -1..1
> >
> > The documentation does not claim that these numbers are the LimInf and
> > LimSup, but I do not know of a case where they are not.
>
> Here's one:
>
> > limit(sin(x)-sin(x)^2, x=infinity);
>
> -2 .. 1
>
> The actual lim sup is 1/4.
This is a further example:
> limit(2*sin(x)*cos(x),x=infinity);
-2 .. 2
> limit(sin(2*x),x=infinity);
-1 .. 1
>
The range computations appear somewhat "rough". At least it appears that the
ranges are - if wrong - always overestmated. Or are there examples, where the
computed ranges are too small?
All the best Jurgen
--
-------------------
Prof. Dr. Jurgen Barsuhn
Fachhochschule Bielefeld
University of Applied Sciences
Fachbereich Elektrotechnik und Informationstechnik
Wilhelm-Bertelsmann-Str. 10
D-33602 Bielefeld
http://infmath.fh-bielefeld.de/
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