Mathematics, 08.04.2020 05:06 vanessa23272

Show that laplace transform StartSet e Superscript at Baseline t Superscript n EndSetℒeattn(s)equals=StartFraction n exclamation mark Over (s minus a )Superscript n plus 1 EndFraction n! (s−a)n+1 in two ways.

(a) Use the translation property for F(s).
(b) Use the formula laplace transform StartSet t Superscript n Baseline f (t ) EndSet (s )ℒtnf(t)(s)equals=(negative 1 )Superscript n Baseline StartFraction d Superscript n Over ds Superscript n EndFraction (laplace transform StartSet f EndSet (s ))(−1)n dn dsn(ℒ{f}(s)).

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Show that laplace transform StartSet e Superscript at Baseline t Superscript n EndSetℒeattn(s)equals...