Analysis Help

Determine whether the following statements are true or false and justify your answers:

1. For all epsilon>0, there exists a natural number N such that

N>=n --> |n(cosh(1 + 1/n) - cosh(1)) - sinh(1)| < epsilon

2. Let {xn} be a bounded real sequence and f: R --> R be continuous. Then {f(xn)} is bounded.

No idea how to do 1. For 2, I was thinking along the lines of Bolzano-Weierstrass but not sure where to go from there.