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Beliebt Rechnen >

laplacetransform (t)e^{4t}

Lösung

laplace transformation

(t) e^{4 t}

Lösung

\frac{1}{( s - 4 ) ^{2}}

Schritte zur Lösung

L {e^{4 t} (t)}

Wende Laplace-Transformationstabelle an:

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

Für

t e^{4 t} : f (t) = e^{4 t}, k = 1

= (- 1)^{1} \frac{d}{d s} (L {e^{4 t}})

L {e^{4 t}} : \frac{1}{s - 4}

\frac{d}{d s} (\frac{1}{s - 4}) = - \frac{1}{( s - 4 ) ^{2}}

= (- 1)^{1} (- \frac{1}{( s - 4 ) ^{2}})

= \frac{1}{( s - 4 ) ^{2}}

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