CalcNotes0208-page7 - (Section 2.8: Continuity) 2.8.7 PART...

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(Section 2.8: Continuity) 2.8.7 PART D: CONTINUITY ON AN OPEN INTERVAL Definition of Continuity on an Open Interval Assume that a and b are real constants such that a < b . A function f is continuous on the open interval a , b () ± f is continuous at every number (point) in a , b . This extends to unbounded open intervals of the form a , ± , ±² , b , or , ² . In Example 6, all three functions are continuous on the interval 0, ± . The first two functions are also continuous on the interval ,0 . We say that the continuity set (in interval form) of the first two functions is ³ 0, ² , because that is the set of all real numbers at which those functions are continuous. (See Footnotes 3 and 5.)
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