Suppose that f(t) and f'(t) both have Laplace transforms that exist for all s > 0. If \lim_{t\to\infty}f(t) exists and \lim_{s\,\to\, 0}{sF(s)} exists then \lim_{t\to\infty}f(t) = \lim_{s\,\to\, 0}{sF(s)}.
