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Q4. (15') (a). Given 10 ~ s(s+1) determine the final result of function f(t) by final value theorem in Laplace transform, then F(s) verify your result through lim f(t). (b). A system has input r(t) = 1(t), output c(t) = 1 e~2! + e~*, and initial conditions of the system are assumed zero, determine the transfer function and impulse response of the system. (c). Given S+2 s(s + 3)(s + 1)? determine the corresponding f(t) by inverse Laplace transform. F(s) =