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Unformatted text preview: Given a real number x, we deﬁned the ﬂoor of x, denoted by x , as the largest integer
smaller than or equal to x. For example, π = 3, 7 = 7, and −0.5 = −1.
(a) At which points is the function f (x) = x continuous?
(b) Consider the function g (x) = sin x . Show that g has exactly one removable and one
non-removable discontinuity inside the interval (0, 2π ). 6. In each of the following questions, we list one or more properties for a function f . For each
question, give us one function that satisﬁes them and ske...
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