#5625 limit(unit_step(x^2-x^3), x, 0, plus) gives ind instead of 1

[David Scherfgen]

By Claude:

For small positive x, x^2-x^3 is positive, so unit_step(x^2-x^3) is 1 near 0 from the right and the limit is 1. limit says ind:

(%i1) limit(unit_step(x^2-x^3), x, 0, plus);
(%o1) ind
(%i2) limit(unit_step(x^3-x^2), x, 0, plus);
(%o2) ind
(%i3) limit(signum(sinh(1/x)-1/x), x, inf);
(%o3) -('limit(signum(1/x-sinh(1/x)),x,inf))

The answers should be 1, 0 and 1. limit finds that the argument tends to 0 but not from which side, because it looks only at the linear term of the argument, and that is 0 here. With a linear term it works:

(%i4) limit(unit_step(x-x^2), x, 0, plus);
(%o4) 1