Question: Suppose f(r) is defined (but not necessarily continuous) on the closed interval [a, b] and suppose that f is nondecreasing on [a, b]. (a)

Suppose f(r) is defined (but not necessarily continuous) on the closed interval

Suppose f(r) is defined (but not necessarily continuous) on the closed interval [a, b] and suppose that f is nondecreasing on [a, b]. (a) Show that f is bounded above and bounded below. (Hint: don't over-think this. It should be easy.) (b) Let c (a, b) be arbitrary. Prove that lim f(a) exists, and prove that lim f(x) exists. 2-c (c) Prove that lim f(x) f(c) lim f(x). 11" zuet

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