SolitaryRoad.com

Website owner: James Miller

[ Home ] [ Up ] [ Info ] [ Mail ]

Prove. Final value theorem. Let L[*F*(t)] = f(s). If *F*(t) and *F *'(t) are both piecewise regular
and of exponential order, and if the abscissa of convergence of *F *'(t) is negative, then

provided these limits exist.

Proof. This theorem is valid whether *F*(t) is continuous at t = 0 or not. For generality we will
assume that it is discontinuous at t = 0.

First note that

Let us now take the limit as s 0.

Now

Substituting 3) into 2) we have

or

SolitaryRoad.com

Website owner: James Miller

[ Home ] [ Up ] [ Info ] [ Mail ]