3t , t2 _ 6t + 8_ 0 t 1 1 t 2 2 t 0 Consider the piecewise function, g(t) Sketch the gra…

3t , t2 _ 6t + 8_ 0 lt; t lt; 1 1 lt; t lt; 2 2 lt;t lt; 0 Consider the piecewise function, g(t) Sketch the graph of g(t). Express g(t) using unit step functions, U(t - a) Apply the translation theorem in 7.3.2 to find the Laplace Transform; G(s) = Lg(t). For each of the transforms G(s), express the inverse transform, g(t) = L- #x27;G(s), in terms of unit step functions; represent g(t) in the usual format for a piecewise function and sketch its graph. 2e S1z G(s) 4+(4+4) e `2 (6) G(s) = 562+1) s(s2 + 1) s(s2 + 1)

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