1- Find the Laplace transform and the corresponding ROC of the following signals. a) x(t) = [et + et cos(3t)]u(t) b)x(t) = e-alte-atu(t) + eatu(-t), consider a>0. c) x(t)=8(t) +8(t-1)+8(t−2) d) x(t) = u(-1)-u(1) e) x(t) = e-³t sin(2t)u(t)dr f)x(t) =[r³ +sin(2t)]u(t)dt g)x(t)=t2e2 cos(5t) u(t - 1)

Express the function below using window and step functions and compute its Laplace transform. 2190 Q 0- 5x 16 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Express g(t) using window and step functions. Choose the correct answer below. A. g(t)= (sin 8t)u t-- (sin 8t)u (1-56) OB. 9(t)=11 sin (81) OC, 9(t) = (sin 8t)II 5x (t) + (sin 8t)u t- 0.7 16 salt) 0.16 I OD. g(t)=(cos 8t)u t-- : 8tu (1-556) 16 Compute the Laplace transform of g(t). L(g) = (Type an expression using s as the variable.)

9. Find the Laplace transform of the waveform shown below a) b) Answer: a) F(s) =[1- e-s - e-3s - e-1$] b) F(s) = [e¬s + e-25 + e-3$ + e-4s - 4e-5s1 %3D

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