Continuity and sequences

Let $val9: $val12 -> $val12 be a real function. Are the following statements justified?

A. If $val31, then $val33.

B. If $val33, then $val31.


Epsilon - Delta

Let be a real function such that:

For all , there exists a such that implies .

What does this mean to the continuity of ?

Epsilon - Delta II

Let be a real function such that:

For all , there exists a such that implies .

What does this mean to the continuity of ?

Mixed multiplication

Let be a real function, Is the following statement true?

If is continuous, then is continuous.


Powers

Let be a real function. Is the following statement true?
If $val11 is continuous, then $val12 is continuous.