Find if it is monotonic, bounded and what the limit is.

Question

Find the limit of the following sequence or determine that the limit does not exist. Prove if it is monotonic, or bounded.

{n sin(7/n)}

 

Thank you

Answer 1

lim(nsin(7/n)) n→∞ = (n = 1/x, x →0) = lim x →0(1/xsin(7x) = lim x →0 7sin(7x)/(7x) = 7·1 = 7