Question

derive laplace formula

Answer 1

Proof of L(t
n
) = n!/s1+n
Slide 1 of 3
The first step is to evaluate L(f(t)) for f(t) = t
0
[n = 0 case]. The function t
0
is
written as 1, but Laplace theory conventions require f(t) = 0 for t < 0, therefore f(t)
is technically the unit step function.
L(1) = R ∞
0
(1)e
−stdt Laplace integral of f(t) = 1.
= −(1/s)e
−st|
t=∞
t=0 Evaluate the integral.
= 1/s Assumed s > 0 to evaluate limt→∞ e
−st

Answer 2

$\textbf{Answer is in Attachment !!}$