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Exercise 3. Using the time scaling property, or otherwise, show that the signal x (t) = eat u(-t) has Laplace transform with Real(s) < Real(a) as the ROC. We will assume that it makes sense to say that the signal x(t) = s(t) has Laplace transform X (s) = 1 with ROC being the entire complex plane. Exercise 4. Using the above Laplace transforms and properties (or otherwise) find the Laplace transforms of the following signals along with their ROCs. A)x(t)=u(t) = r(t)=(t+1)u(t-2) D) E) (t)=eat cos(wt)u(t)where a and w are fixed real numbers. F)x(t)=eat sin(w(t+2))u(t-1)where - O and w are fixed real numbers. G) with Real (a) < Real(b). What happens if Real(a) > Real(b)? H) r(t) =e-a/t/ with Real(a) > 0. What happens if Real(a) <0? What does this problem have to do with part G)?

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