could someone give me the example that the function is:

A) regulated and discontinuous

B)not regulated and discontinous

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- Dec 9th 2012, 10:37 AMcummings123321regluated and continous function example
could someone give me the example that the function is:

A) regulated and discontinuous

B)not regulated and discontinous - Dec 9th 2012, 02:26 PMPlatoRe: regluated and continous function example
I had to look up that term. I have always called such functions quasi-continuous.

For A, use any step function. For example the floor function on $\displaystyle [0,10]$.

For B, use any discontinous function which is not of bounded variation.

Here is a function which is continuous but not q-continuous.

$\displaystyle \left\{ {\begin{array}{rr} {x^2 \sin \left( {\frac{1}{{x^2 }}} \right),} & {x \ne 0} \\ {0,} & {x = 0} \\ \end{array} } \right.$