Which one of the following statements is true?
A. The convolution property of Laplace transforms says that L[f(t)g(t)] = F(s) + G(s)
B. If the function f is piecewise continuous for t ≥ 0 and is of exponential order as t → ∑, then its Laplace transform F(s) = L[f(t)] exists.
C. If F(s) = L[f(t)], G(s) = L[g(t)] and F(s) = G(s) then it must be the case that f(t) = g(t).
D. If f(t) is piecewise continuous, but not continuous on [0, ∑) then
L[f'(t)] = sF(s) - f(0)
E. There are no F(s) 's where
lim s→0 F(s) ≠ 0