Question 1 Use table-lookup method to find the Laplace transform F (s) of the following functions in / domain : (a) f(1) = (2+41+2)@" (5%) (b) f(1) =be" cos 21-elf (5 %) (c) f(1) = sint [ HINT : cos 2/ = cos' / - sin ; sin / + cos? ( = 1 ] (10 % )Laplace and Inverse Laplace Transforms First and second order transformation: L{ f' (t) } = sF(s) - f(0) ; L { f (t) )= s' F(s) - s f(0) -f(0) Laplace Transforms Inverse Laplace Transforms F(S) L' (FS) = f(0 a 1" (n is a positiveinteger) (n -1)! sin cof (s tal coscor sin of sinh or cosor cosh or "sin of ( sta)to s+ a cosof ( sta)to sinh or - at cosh of "sinh ox stay -0 sta coshot (sta) - c 2 ax fsincor I cos or (s' + 6)