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Beliebt Rechnen >

laplacetransform f(t)=t^2+6t-3

Lösung

laplace transformation

f (t) = t^{2} + 6 t - 3

Lösung

\frac{2}{s ^{3}} + \frac{6}{s ^{2}} - \frac{3}{s}

Schritte zur Lösung

L {t^{2} + 6 t - 3}

Verwende die lineare Eigenschaft der Laplace-Transformation:

Für Funktionen

f (t), g (t)

und Konstanten

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {t^{2}} + 6 L {t} - L {3}

L {t^{2}} : \frac{2}{s ^{3}}

L {t} : \frac{1}{s ^{2}}

L {3} : \frac{3}{s}

= \frac{2}{s ^{3}} + 6 \cdot \frac{1}{s ^{2}} - \frac{3}{s}

Fasse

\frac{2}{s ^{3}} + 6 \frac{1}{s ^{2}} - \frac{3}{s}

zusammen:

\frac{2}{s ^{3}} + \frac{6}{s ^{2}} - \frac{3}{s}

= \frac{2}{s ^{3}} + \frac{6}{s ^{2}} - \frac{3}{s}

Beliebte Beispiele

tangent f(x)=2x^4,(-2,32)

t an g e n t f (x) = 2 x^{4}, (- 2, 32)

derivative of 18xe^{x^2}

\frac{d}{d x} (18 x e^{x^{2}})

integral of 3e^x-sin(x)

\int 3 e^{x} - sin (x) d x

limit as n approaches infinity of ((cos(1/n)-1))/(1/n)

n \to \infty lim (\frac{( cos ( \frac{1}{n} ) - 1 )}{\frac{1}{n}})

integral of (r^2-10r+4)/(r^3)

\int \frac{r ^{2} - 10 r + 4}{r ^{3}} d r