# Final Value Theorem (FVT)

Learned in MATH213.

Theorem 3: Final Value Theorem

For a function $F(s)$, if

- is a proper rational function
- has the property that all the poles have real parts that are strictly negative with the exception of a single pole (of order 1), i.e. $sA $, at $s=0$
or if $F(s)$ is the product of a function satisfying the above conditions multiplied by a complex exponential $e_{sT}$ , then $lim_{t→∞}f(t)=lim_{s→0}sF(s)$

If the poles of a rational function do not satisfy the above condition, then $lim_{t→∞}f(t)$ does not exist.

If the

`F`

does not satisfy those two conditions...Then you say that the limit does not exist.