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## Re: [Axiom-developer] wrong sign in limit?

**From**: |
Waldek Hebisch |

**Subject**: |
Re: [Axiom-developer] wrong sign in limit? |

**Date**: |
Thu, 30 Sep 2010 15:21:19 +0200 (CEST) |

Dr.-Ing. Ingo D. Rullhusen wrote:
>* *
>* Hello,*
>* *
>* perhaps i have found a bug in the limit operation. I am using*
>* *
>* AXIOM Computer Algebra System*
>* Version: Axiom (July 2010)*
>* Timestamp: Wednesday August 18, 2010 at 11:16:49*
>* *
>* on a x86_64 with linux. There seems to be an error in the sign, if you*
>* compare the limit result with the de L'Hospital one.*
>* *
>* *
>* Z:=sqrt(a^2+h^2)-a*
>* *
>* N:=a*sqrt(a^2+h^2) - a^2 - h^2*
>* *
>* limit( Z/N, h=0 )*
>* *
>* *
>* 1*
>* (3) -*
>* a*
>* Type: Union(OrderedCompletion Expression*
>* Integer,...)*
>* *
>* -- this seems to be wrong!*
>* -- because de L'Hospital says*
>* *
>* dZ:=differentiate( Z, h, 2 )*
>* *
>* dN:=differentiate( N, h, 2 )*
>* *
>* eval(dZ/dN,h=0)*
>* *
>* *
>* 1*
>* (6) - ----------*
>* +--+*
>* | 2*
>* 2\|a - a*
>* *
>* (see sign)*
Square root has two branches, the result depends on which branch
you choose. Limit decided that sqrt(a^2) = -a and the result
is correct for this branch (and wrong for the other branch).
de L'Hospital rule can be used only when limit on N is 0, which
hold when sqrt(a^2) = a, but the result is wrong for the other
branch. If you want result which is correct for both branches
you need something like:
-sqrt(a^2)/a^2
but such expressions cause trouble so limit decided just to pick
one branch...
--
Waldek Hebisch
address@hidden