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and discontinuity of a function are concepts defined only for points in the function's domain.

Jump discontinuity

Consider the function

Then, the point is a '.

In this case, a single limit does not exist because the one-sided limits, and exist and are finite, but are not equal: since, the limit does not exist. Then, is called a jump discontinuity, step discontinuity, or discontinuity of the first kind. For this type of discontinuity, the function may have any value at

Essential discontinuity

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