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OEF continuity

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
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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Description: collection of exercises ont the continuity of functions of one real variable. Serveur Wims de l'ESPE-Nice-Toulon - Université de Nice - Sophia Antipolis

Keywords: interactive mathematics, interactive math, server side interactivity, analysis, continuity,limit,sequence,real_function, calculus