MATH 132 Lecture 3: CLASS NOTES -- 9.2 -- Continuity
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18 Sep 2016
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Definition: a function, f, is continuous at x= c if all three of the following conditions are met: f x exists, f c exists, and f x f c lim c x lim c x. If any one or more of these conditions are not met, then we say f is discontinuous at x = c. 1 is discontinuous at x = 1, because, when x = 1, the denominator is zero. Therefore there is no y-coordinate when x = 1, i. e. both have a factor of x 1, f x lim x. The domain of f is r except x = 4 and x = 5. Therefore f is continuous for all real values of x except 4 and 5. Another way of writing this would be: f is continuous over the intervals ___________________________________________________. f x x= - So far we"ve looked at and evaluated limits as x approached a particular value.
