For problems # 1 - 5 show the Laplace Transform for the given function is what the chapter states (1) Use integration by parts and the definition of the Laplace transform to justify why L{y'} = s£{y} − y(0) for s> 0 whenever y(t) is bounded. 2 (2) Show that L[r²e²](s) = (s-²1)³ · (3) Show that L[cos(t)](s) = $²+1 (4) Show that L[u(v − 2)](s) = e−²³. (5) Show that L[u(x - 3)x](s) -38 e +3se-3s 82 Solution Solution Solution Solution Solution

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