For each of the following sequences, decide if it converges or not. If it converges, find its limit. 1. The sequence {an};:=1 given by an=n2/e'\" . Hint: Consider some useful function f(a:) and perhaps L'Hospital rule might help. 2. The sequence {adil given by an =sin(n) n2 n + 3 3. The se uence a \"L iv b = q { n}n_1 9 en 37 an V 3n2 n +1 arctan n) "'1 5. The sequence an = given by an =nsin n 1 n 4. The sequence {an,};=1 given by a,\" 6. The sequence {a,,,}ff'=1 given by an = {/5 7 . The sequence {adil given by an = n Vn + lxln + 3