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Beliebt Rechnen >

laplacetransform t^2t^3

Lösung

laplace transformation

t^{2} t^{3}

Lösung

\frac{120}{s ^{6}}

Schritte zur Lösung

L {t^{3} t^{2}}

Wende Laplace-Transformationstabelle an:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

Für

t^{2} t^{3} : f (t) = t^{3}, k = 2

= (- 1)^{2} \frac{d ^{2}}{d s ^{2}} (L {t^{3}})

L {t^{3}} : \frac{6}{s ^{4}}

\frac{d ^{2}}{d s ^{2}} (\frac{6}{s ^{4}}) = \frac{120}{s ^{6}}

= (- 1)^{2} \frac{120}{s ^{6}}

= \frac{120}{s ^{6}}

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