OEF continuity --- Introduction ---

This module actually gathers 5 exercises on the continuity (definition and fundamental properties) of functions of one real variable.

Continuity and sequences

Let be a real function. Are the following statements justified?

A. If , then .

B. If , then .

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:
, , such that .
What does this mean to the continuity of ?

Mixed multiplication

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

Powers

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