1. Using limit laws or otherwise prove the following: a) lim(n +nn)=- b) lim(2" 3")" =3 2 4 2. Suppose lims,, = 1. Prove that there exists N = N such that S,, > for all n > N. 5 3. Prove that a set S is dense in R if and only if each x = R is a limit of a sequence in S.