Question 1: (a) x(t) =2t[u(t-2)-u(t-5)] Figure-a ( b) x(t) = 3e-[u(t) -u(t -3)] (c) Waveform given in Figure-a (i) Use the definition of the Laplace Transform (LT) to find the LT w. of the time functions (a), (b) and (c). Sketch the time function 6 and region of convergence (ROC). (ii) Verify transformation using the LT and properties table for time functions (a), (b) and (c). Answers: (a) X(s) = N / N (2s + 1)e-25 - (5s + 1)e-5s , Re(s) > 0 3 (b) X(s) = s+5 (1-e-3 (5+5 ) , Re ( s ) > - 5 Ites e 4s _-6s (c) X(s) = Re(s) > 0 S $ 2