#4048 An incorrect limit

[Emmanuel Charpentier]

Inspired by this ask.sagemath.org question. Consider :

(%i1) display2d:false;

(%o1) false
(%i2) define(f(x),diff(log(tan(%pi/2*tanh(x))),x));

(%o2) f(x):=(%pi*sech(x)^2*sec((%pi*tanh(x))/2)^2)/(2*tan((%pi*tanh(x))/2))
(%i3) limit(f(x), x, inf);

(%o3) und
(%i4) limit(trigreduce(trigsimp(trigreduce(f(x)))), x, inf);

(%o4) 2

As documented in the inspirating post's comments, he first answer is incorrect, the second one is correct.

HTH,

[Stavros Macrakis]

Yes, and other ways of simplifying also lead to the correct answer:

f: diff(log(tan(%pi/2*tanh(x))),x);
makelist(limit(simpfun(f),x,inf),simpfun,'[exponentialize,trigreduce,trigrat]) 
    => [2,2,2]

[David Scherfgen]

Fixed by commit [92e5f8].