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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- October 9th 2009, 11:32 AMzhupolongjoeProof...monotonicity
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 - October 9th 2009, 12:45 PMPlato
- October 10th 2009, 11:10 AMzhupolongjoe
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