M251.012, 016 Quiz 4A due on Mon Oct 30 in Class F2017 NAME/Section ( 3t3 2t, if 0 t < 7, Check that the Laplace 1. (3 points) Set: f (t) = 1, if t 7. transform F (s) = L{f (t)} is \u0012 \u0013 18 2 18 126 542 1083 F (s) = 4 3 e7s + + + . s s s4 s3 s2 s 2. (3 points) Suppose that L{f (t)} = F (s). Check that h i L{t2 e1+2t f 00 (t)} = 2F (s 2) + 4(s 2)F 0 (s 2) + (s 2)2 F 00 (s 2) e. 3. (3 points) Find the inverse Laplace transform L1 n e3s+5 (3s2 2) o . s3 4s2 n o n o 4. (.5 point for each) T or F: (A) L1 F (s) + 5 = L1 F (s) + 5? n o n o (B) L1 F (s) + 5es = L1 F (s) + (t 5)? 1