Laplace's Transform: Initial-value Theorem applied to the n-th derivative

[libelec]

Homework Statement

Prove that, under the right assumptions, lim_{s tends to infinity} sⁿ⁺¹F(s) = f⁽ⁿ⁾(0+)

The Attempt at a Solution

I don't have a problem with the common initial-value theorem, under the assumptions that both f and f' are partly continuous and of exponential order. Then I can find that the absolute value of sF(s) tends to f(0+).

But for f⁽ⁿ⁾(t), the Laplace's transform is sⁿ⁺¹F(s) - [sⁿf(0+) + s^n-1f'(0+) + ... + f⁽ⁿ⁾(0+)].

Should I make the assumption that all initial values except for f⁽ⁿ⁾(0+) are equal to zero?

 

[libelec]

Anybody?