Hey.

I have played around with this question for my analysis class and I would like some help:

Given: L= lim f1(x), M=lim f2(x)

Show that if f1<=f2 for all x in some interval (a,b), then L<=M

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- Nov 24th 2008, 05:52 AMUriahLimit Analysis Question
Hey.

I have played around with this question for my analysis class and I would like some help:

Given: L= lim f1(x), M=lim f2(x)

Show that if f1<=f2 for all x in some interval (a,b), then L<=M - Nov 24th 2008, 06:07 AMOpalg
It's probably easiest to do this by contradiction. Suppose that L>M and let . For x sufficiently close to some limit point c (the limit point isn't specified in the question), it will be true that and . From that, and the fact that , you should be able to use the triangle inequality to get a contradiction.

- Nov 24th 2008, 07:57 AMUriah
I am still struggling here. I can't find a way to make the triangle inequality work for this because if I use it on or I know nothing about the relationship between and epsilon.

- Nov 24th 2008, 08:53 AMOpalg
- Nov 24th 2008, 09:42 AMUriah
Duh. I can't believe I didn't look at it like that. Thanks!