Let f:[a,b]--->R be monotone. Prove that f has a limit at BOTH a and b. I have no idea what to do. Please help. Thanks
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Originally Posted by zhupolongjoe Let f:[a,b]--->R be monotone. Prove that f has a limit at BOTH a and b. Let's assume that is nondecreasing. The set is bounded below by . So let . Show that is limit as .
Ok, so do I just show that using the limit definition or is there some other trick? After that, I assume I should make T={f(x): x is in (a,b)} bounded above by f(b) And then have L2=sup(T) and show L2 is the limit as x--->b-? Thanks
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