initial-value theorem

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initial-value theorem [i′nish·əl ¦val·yü ‚thir·əm]

(mathematics)

The theorem that, if a function ƒ(t) and its first derivative have Laplace transforms, and ifg(s) is the Laplace transform of ƒ(t), and if the limit ofsg(s) assapproaches infinity exists, then this limit equals the limit of ƒ(t) astapproaches zero.

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