(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that, under the right assumptions, lim_{s tends to infinity}s^{n+1}F(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 s^{n+1}F(s) - [s^{n}f(0+) + s^{n-1}f'(0+) + ... + f^{(n)}(0+)].

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

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

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