Prove the following by using this definition:

A sequence (Sn) is said to converge to the real number S provided that for each e > 0 there exists a real number N such that for all n element of N, n > N implies that |Sn - S| < e

If (Sn) converges to S, then S is called the limit of sequence (Sn), and we write lim n -> infinity Sn = S, lim Sn = S, or Sn -> S. If a sequence does not converge to a real number, it is said to diverge

Prove this from the definition above:

a) lim (3n + 1)/(n + 2) = 3

b) lim (sin n) / n = 0

c) lim (n+2)/(n^2 - 3) = 0