Limit distinguishes between inf (infinity approached along the
positive real axis), minf (negative real), and infinity (complex
infinity). Thus:
limit(2^n,n,inf) => inf
limit(2^n,n,infinity) => und
limit(sin(x)/x,x,inf) => 0
limit(sin(x)/x,x,infinity) => und (correct: goes to inf along
imaginary axis)
Not that this functionality is very complete, e.g.
limit(abs(x)/x,x,inf) => 1 (OK)
limit(abs(x)/x,x,infinity) => infinity (should be complex ind,
which we don't have)
limit(abs(x)/(abs(x)+1),x,inf) => 1
limit(abs(x)/(abs(x)+1),x,infinity) => noun form (should be 1)
Limit also allows specifying directional limits at finite points:
limit(1/x,x,0) => und (could be infinity)
limit(1/x,x,inf,plus) => inf
limit(1/x,x,inf,minus) => minf
but it doesn't support complex limits at finite points -- the
workaround is to move the point to infinity, e.g.
limit(1/(1/x),x,infinity) => infinity