In Maxima 5.11.0:
tlimit(s/(1+s^2)/sinh(x*T), s, inf);
Is T positive, negative, or zero?
p
Invalid call to var-expand.
(Cf. Maxima list: March 31, 2007, "bug in tlimit?").
Stavros mentioned on the list that
taylor(exp(x)-exp(-x), x, inf, 2) returns a sensible result whereas taylor((exp(x)-exp(-x))/2, x, inf, 2)
triggers an internal error.
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fixed in hayat.lisp rev 1.27
(%i21) tlimit(s/(1+s^2)/sinh(x*T), s, inf);
Is x*T positive or negative?
pos;
(%o21) 0
(%i22) taylor((exp(x)-exp(-x))/2, x, inf, 2);
(%o22) 1/(2*%e^-x)-%e^-x/2