Question

prove final value theorem

Answer 1

to prove final value theorem first i'm assuming the function f(t) is laplace transformable and f'(t) is also laplace transformable
and also \[sF(s)\] has no poles in (jw) axis

Answer 2

I see, in other word it is stable

Answer 3

yes stable :)
now
from differentiation rule--
\[\huge \int\limits_{0^-}^{\infty}f'(t)e^{-st}=sF(s)-f(o-)\]
ok?

Answer 4

now we have to take limit as \[s \rightarrow0\]