Prev: Limits for periodic functions
Next: ROM for 50G
From: supergems on 8 Jun 2010 08:44
Read this discussion: http://groups.google.com/group/comp.sys.hp48/browse_thread/thread/3da4c3b04a0ee61a

and remember that 'lim(F(Z),ABS(Z)=\oo)' = 'lim(F(1/Z),ABS(Z)=0)' ;-)
From: Virgil on 9 Jun 2010 01:01
In article <87eigh695s.fsf(a)merciadriluca-station.MERCIADRILUCA>,
Merciadri Luca <Luca.Merciadri(a)student.ulg.ac.be> wrote:

> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>
> Virgil <Virgil(a)home.esc> writes:
>
> > In article <87typf11fa.fsf(a)merciadriluca-station.MERCIADRILUCA>,
> > Merciadri Luca <Luca.Merciadri(a)student.ulg.ac.be> wrote:
> >
> >> -----BEGIN PGP SIGNED MESSAGE-----
> >> Hash: SHA1
> >>
> >> Virgil <Virgil(a)home.esc> writes:
> >>
> >> > In article <87k4qcb9cx.fsf(a)merciadriluca-station.MERCIADRILUCA>,
> >> > Merciadri Luca <Luca.Merciadri(a)student.ulg.ac.be> wrote:
> >> >
> >> >> -----BEGIN PGP SIGNED MESSAGE-----
> >> >> Hash: SHA1
> >> >>
> >> >> Hi,
> >> >>
> >> >> One can define sin(z), z being a complex number. How can the HP50g
> >> >> compute the limit of sin(z) when z approaches the positive infinity?
> >> >
> >> > Along what path?
> >> >
> >> > As far as I can see, there is no Z path towards positive real infinity
> >> > along which SIN(Z) would even have a limit.
> >> Sorry, I forgot to mention that this is not z, but |z|, and for
> >> |(sin(z))/[(z^2 + a^2)^2]|. But if I
> >> take a correct limit (i.e. one which exists), how can I compute it
> >> with the 50g?
> >> >
> >> >> (I.e. what could I type to achieve this?) I can evidently compute
> >> >> limits for real-valued functions, with the HP50g, but I never tried
> >> >> (and I don't know how to do it) with complex functions.
> >
> > If the limit exists at all, it will exist along every complex path from
> > z = 0 to |z| = oo.
> >
> > So to start with try it along each of the paths from 0 towards oo along
> > one of the axial directions of the complex plane:
> > t, -t, i*t and -i*t as real t goes towards oo.
> > For each of those, you can work out explicit real expressions for
> > |(sin(z))/[(z^2 + a^2)^2]|
> >
> > If all 4 have limits and are equal then there may actually be a limit
> > for arbitrary paths
> Yes, but I thought that the HP50g could have been able to try for all
> the axial directions of C^2!

It can, but only one at a time.
From: Merciadri Luca on 9 Jun 2010 16:41
-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

Thanks all.

- --
Merciadri Luca
See http://www.student.montefiore.ulg.ac.be/~merciadri/
- --

Don't judge a man by the size of his hat, but by the angle of his
tilt.
-----BEGIN PGP SIGNATURE-----
Version: GnuPG v1.4.9 (GNU/Linux)
Comment: Processed by Mailcrypt 3.5.8 <http://mailcrypt.sourceforge.net/>

iEYEARECAAYFAkwP/JQACgkQM0LLzLt8MhzUgwCfZCeZaM2NV3eAP/JN9pukSCn+
lK8Anichyb9fFUXiVcuZS3jbnqCQTiax
=5mAw
-----END PGP SIGNATURE-----
First  |  Prev  | 
Pages: 1 2
Prev: Limits for periodic functions
Next: ROM for 50G