Solutions of Sample Problems for Third In - Class Exam
نویسنده
چکیده
(1) Compute the Laplace transform of f (t) = t e 3t from its definition. Solution. The definition of the Laplace transform gives L[f ](s) = lim T →∞ T 0 e −st t e 3t dt = lim T →∞ T 0 t e (3−s)t dt. This limit diverges to +∞ for s ≤ 3 because in that case T 0 t e (3−s)t dt ≥ T 0 t dt = T 2 2 , which clearly diverges to +∞ as T → ∞. For s > 3 an integration by parts shows that T 0 t e (3−s)t dt = t e (3−s)t
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