#1423 strange limit result

[Anonymous]

/*wxMaxima 0.7.5 http://wxmaxima.sourceforge.netMaxima 5.15.0 http://maxima.sourceforge.netUsing Lisp GNU Common Lisp (GCL) GCL 2.6.8 (aka GCL)Distributed under the GNU Public License. See the file COPYING.Dedicated to the memory of William Schelter.The function bug_report() provides bug reporting information.

(%i1) abs(sin(x))/sqrt(1-cos(x));
(%o1) abs(sin(x))/sqrt(1-cos(x))
(%i2) limit(%o1, x, 0, minus);
(%o2) -sqrt(2)
(%i3) limit(%o1, x, 0, plus);
(%o3) sqrt(2)
(%i4)
bug_report()$The Maxima bug database is available at http://sourceforge.net/tracker/?atid=104933&group_id=4933&func=browseSubmit bug reports by following the 'Submit New' link on that page.Please include the following build information with your bug report:-------------------------------------------------------------Maxima version: 5.15.0Maxima build date: 17:36 4/20/2008
host type: i686-pc-mingw32
lisp-implementation-type: GNU Common Lisp (GCL)lisp-implementation-version: GCL 2.6.8-------------------------------------------------------------The above information is also available from the Maxima function build_info().(%i5)

amedeo.maddalena@unipd.it

[Dan Gildea]

Logged In: YES
user_id=1797506
Originator: NO

In current cvs:

(%i2) limit(sin(x)/sqrt(1-cos(x)), x, 0, plus);
(%o2) sqrt(2)

OK

(%i3) limit(sin(x)/sqrt(1-cos(x)), x, 0, minus);
(%o3) sqrt(2)

Should be -sqrt(2). In both cases, limit is using taylor:

(%i4) taylor(sin(x)/sqrt(1-cos(x)), x, 0, 3);
(%o4) sqrt(2)-sqrt(2)*x^2/8

This fits one side of the discontinuity. What is the correct
behavior for taylor in this situation?

[Dan Gildea]

Fixed using gruntz algorithm in limit.lisp rev 1.60.