laplacetransform f(t)=e^{2(t-2)}

Lösung

laplace transformation

f (t) = e^{2 (t - 2)}

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

Schritte zur Lösung

L {e^{2 (t - 2)}}

Schreibe

e^{2 (t - 2)}

um:

e^{2 t - 4}

= L {e^{2 t - 4}}

Verwende die konstante Multiplikationseigenschaft der Laplace-Transformation:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= e^{- 4} L {e^{2 t}}

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

= e^{- 4} \frac{1}{s - 2}

Fasse

e^{- 4} \frac{1}{s - 2}

zusammen:

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

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

d er i v a t i v e f (x) = \frac{1 + x}{( 2 x ^{2} + 1 ) ^{2}}

\frac{d}{d t} (t^{3} - 5 t^{2} + 9 t)

a re a y = 2 x + 2, y = x^{2} - 2

a re a y^{2} = 2 x, y = - 4 + x

\int \frac{1}{25 - 4 x ^{2}} d x