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[MUG] Re: Limit Superior & Limit Inferior
| [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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