Answer each of the questions on your own paper. Put your name on each page of your paper. Be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. The laplace transform of f is the function f (s) de ned as follows: 0 e stf (t) dt for all s su ciently large. (b) using your de nition compute the laplace transform of f (t) = 3e 5t + 2. 2 s s + 5 e st dt: [21 points] compute the laplace transform of each of the following functions. You may use the attached tables, but be sure to identify which formulas you are using by citing the number(s) in the table. (a) f1(t) = e 2t(3t4 + 5 cos 3t) Solution. f1(t) = 3t4e 2t +5e 2t cos 3t so f1(s) = 3.