# Epsilon --- Introduction ---

This is an exercise on the definition of continuity

A function $f$ is continuous on a point ${x}_{0}$ if

For all $\epsilon >0$, there exists a $\phantom{\rule{thickmathspace}{0ex}}\delta >0$, such that $\mid x-{x}_{0}\mid <\delta$ implies $\mid f\left(x\right)-f\left({x}_{0}\right)\mid <\epsilon$.
Given a concret function (who is continuous), a ${x}_{0}$ and a $\epsilon >0$, you have to find a $\delta >0$ which verifies the above condition. And you will be noted according to this $\phantom{\rule{thickmathspace}{0ex}}\delta$: more it is close to the best possible value, better will be your note.
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Other exercises on: Continuity   Limit   Analysis   Calculus

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Description: on the definition of continuity: given epsilon, find delta. interactive exercises, online calculators and plotters, mathematical recreation and games

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