a) Given that show that b) Show that c) Use the result of (b) to find l5t l5t sin
Chapter 12, Problem 12.21(choose chapter or problem)
a) Given that \(F(s)=\mathscr{L}\{f(t)\}\), show that
\(-\frac{d F(s)}{d s}=\mathscr{L}\{t f(t)\}\).
b) Show that
\((-1)^{n} \frac{d^{n} F(s)}{d s^{n}}=\mathscr{L}\left\{t^{n} f(t)\right\}\).
c) Use the result of (b) to find \(\mathscr{L}\left\{t^{5}\right\}, \mathscr{L}\{t \sin \beta t\}\), and \(\mathscr{L}\left\{t e^{-t} \cosh t\right\}\).
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