spurious limit computation

[kcrisman]

From this sage-support thread:

     sage: assume(x, 'real')
       sage: limit((x^(1/x)-1)*sqrt(x), x=infinity)
       +Infinity
       sage: limit(((1/x)^x-1)/sqrt(x), x=0, dir='+')
       +Infinity


Thanks.  In pure Maxima we get:

(%i3) limit((x^(1/x)-1)*sqrt(x),x,inf);
(%o3)                                 inf
(%i4) limit((x^(1/x)-1)*sqrt(x),x,0);
(%o4)                                 und
(%i5) limit((x^(1/x)-1)*sqrt(x),x,0,plus);
(%o5)                                  0
(%i6) limit((x^(1/x)-1)*sqrt(x),x,0,minus);
(%o6)                                 inf

From what I understand, the first of these is wrong, maybe also the last (should it be infinity (complex infinity) instead?).


Interestingly,

(%i7) domain:complex;
(%o7)                               complex
(%i10) limit((x^(1/x)-1)*sqrt(x),x,0,minus);

;;;
;;; Detected access to protected memory, also kwown as 'bus or segmentation fault'.
;;; Jumping to the outermost toplevel prompt

<lots of times>

Segmentation fault: 11

Upstream: Not yet reported upstream; Will do shortly.

Component: calculus

Keywords: limit

Issue created by migration from https://trac.sagemath.org/ticket/20452

[fchapoton]

Changed keywords from none to limit