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Problem 3: Consider a continuous function x(t), defined for t 0. The Laplace Transform (LT) for x(t) is defined as: X(s) - Ix(t)e-st dt. Derive the following properties: a) LT(6(t))-1, the ?(t) is the Dirac-delta function b) LT(u(t))-1/s, where u(t) is the unit-step function c) LT(sin(wt))-u/(s2 + ?2) d) LT(x(t-t)u(t-t)) = e-stx(s), ? > 0. e LT(tx)-4x(s).

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