If \(F(s)\) is the Laplace transform of the function
\[
f(t)=e^{-3t}(2\cos5t-3\sin5t),
\]
then \(F(0)=\_\_\_\_.\)
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Use the first shifting theorem:
\[
\boxed{
\mathcal{L}\{e^{-at}f(t)\}=F(s+a)
}
\]
Always verify the options if the computed value differs from the official key.