Problem 1. Find the Laplace transforms of the following functions and determine where it exists: i) f(t) = e- sin 2t (Use the definition, not the table below.) ii ) f ( t ) = 1-t if0 0 eat s-a ' s > a the, n = 1, 2, ... n! sn+1, S > O sin bt b $2+62 , S > 0 cos bt S $2462 , S > O eattn n = 1, 2, ... n! (s- anti , s > a eat sin bt b (s-a) 2462 , s > a eat cos bt s - a (s-a) 2462 , s > a