I'm taking a new class and instructor isn't very helpful . These are probably very simple, but I'm lost.

1) If an-->L, then |an|-->|L|

2) Prove that lim(an-bn) = lim(an)-lim(bn), provided lim(an) and lim(bn) exist

3) Give an example where lim(an) and lim(bn) do not exist, but lim(an+bn) exists.

4) If {an} is a bounded sequence and if {bn} is a sequence converging to 0, then {anbn} converges to 0.

I have tons of questions, but I'll start with these.

Help is extremely appreciated!