I stumbled on the following bug in limit.
Let f and x in f(x) both be unassigned names:
limit( f(x)*exp(-x), x=infinity);
Maple answers 0, but should obviously return unevaluated.
It seems that when it doesn’t know enough about f(x), then it returns zero:
limit( -I*erf(I*x)*exp(-x), x=infinity);
returns 0, but should return infinity (or unevaluated).
The procedure for limit is complicated. I didn’t get very far in tracking the bug, but did find that
`limit/series`( f(1/x)*exp(-1/x),x,right);
correctly returns FAIL. `limit/series` is called from within `limit/limit` which in turn
is called from limit.
The bug
limit( -I*erf(I*x)*exp(-x), x=infinity); 0
may be due to the following feature
limit( f(x)*g(x), x=0); f(0)g(0)
which e.g. results in
limit( f(x)*x, x=0); 0
I would prefer that all three returned unevaluated.