I'm having trouble looking at two problems dealing with sequence limits in advanced calculus. here they are:

A: Suppose that the sequence converges to a nonzero constant . Prove that if , we have , where t is a fixed real number satisfying . Is this statement true if ? How about Explain.

I have looked at if , it is not true because , and if , then it is true, . writing the proof has me confused.

B: Prove that if a sequence converges to 0, and a sequence is bounded, then the sequence converges to 0.

I have looked at using the theorem that states if , but it requires that converges to , what other methods should I use?