let be a function f(t) , and i want to prove that [tex] f(t)=O(t) [/tex] in big-O notation.(adsbygoogle = window.adsbygoogle || []).push({});

i know that Laplace transform of f(t) is F(s) then i perform the integral

[tex] F(s)= \int_{0}^{\infty} dt f(t) e^{-st} [/tex] if we assume f(t)=O(t) then

[tex] F(s)= \int_{0}^{\infty} dt f(t) e^{-st} \le \int_{0}^{\infty} dt e^{-st}t [/tex]

so it would be enough that [tex] F(s) \le Cs^{-2} [/tex] for a positive constant 'C'

is this enough ?

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# Laplace transform

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