laplacetransform t^2+6t-3

Lösung

laplace transformation

t^{2} + 6 t - 3

\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}

t an g e n t f (x) = 3 - 4 x^{2}, - 61, at x = 4

\int 2 x^{3} + 4 d x

x \to 8 - lim (\frac{x + 7}{x + 8})

\int \frac{1}{4 - ( x - 1 ) ^{2}} d x

\frac{d y}{d x} y = (5 - x)^{633}