(Section 2.8: Continuity) 2.8.7 PART D: CONTINUITY ON AN OPEN INTERVALDefinition of Continuity on an Open IntervalAssume that aand bare real constants such that a<b. A functionfis continuous on the open interval a,b()±fis 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 ³0,², because that is the set of all real numbers at which those functions are continuous. (See Footnotes 3 and 5.)
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