a) Let {x_n} be a bounded sequence. Prove that if limn sup |x_n| = 0, then limn x_n exists and equals 0.

(b) Prove that a bounded sequence that does not converge always has at least two subsequences that converge to different limits.

1. (c) Find the limit inferior and limit superior of the sequence {a_n} if a_n = sin n for all n N.
2. (d) Find the set of all subsequential limits for the sequence {x_n} if for all n N