final-value theorem

final-value theorem

[¦fīn·əl ¦val·yü ¦thir·əm]
(mathematics)
The theorem that if ƒ(t) is a function which has a Laplace transform F (s), and if the derivative of ƒ(t) with respect to t is also Laplace transformable, and if the limit of ƒ(t) as t approaches infinity exists, then this limit is equal to the limit of sF (s) as s approaches zero.