Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms If F(s) = £{f(t)} and n = 1, 2, 3, . . ., then £{t^f(t)} = (-1) d _F(s). ds" Evaluate the given Laplace transform. (Write your answer as a function of s.) {3t² cos(t)}

THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{f{t)} and n = 1, 2, 3, .. .,then LRt)} = (-1) F5). ds" Evaluate the given Laplace transform. (Write your answer as a function of s.) L(te" sin(4t)} [(s-2) -16

Find the inverse Laplace transform of the following functions: (a) F(s): 3s+6 s2+3s' (b) F(s) = s2+1 s(s+1)2 · Your answer must contain detailed explanation, calculation as well as logical argumentation leading to the result. If you use mathematical theorem(s)/property(-ies) that you have learned par- ticularly in this unit, clearly state them in your answer.

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