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

1. Jan 14, 2010

### libelec

1. The problem statement, all variables and given/known data

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

3. 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+) + sn-1f'(0+) + ... + f(n)(0+)].

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

2. Jan 15, 2010

Anybody?