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Old September 4th, 2008, 07:54 PM
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Default For those that never learnt well the epsilon-delta proofs

I attach a paper based in how to prove limits by definition, pretty nice.

Hope it helps.
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File Type: pdf epsilondelta.pdf (71.2 KB, 2357 views)
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Old September 4th, 2008, 08:30 PM
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Thanks both my teacher at the high school and university level for some reason never thought this was important and just went directly to limits and derivatives without teaching the proofs.
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Old October 2nd, 2008, 06:46 PM
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LOL THANK YOU! my teacher was unclear about this...
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Old November 30th, 2008, 06:51 PM
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Never has it been more clear...thank you so much. Now the definition of a limit in 3-D makes so much more sense. You are a saint for posting this! SO useful!
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Old February 9th, 2009, 01:00 AM
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jajaj Krizalid thank you very much, as always, excellent input.
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Old February 9th, 2009, 03:34 AM
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here's something for practice: using \epsilon-\delta method, directly prove that:

calculus 1: if p(x) is a polynomial, then \lim_{x\to a}p(x)=p(a).

calculus 2: if p(x,y) is a polynomial, then \lim_{(x,y) \to (a,b)}p(x,y)=p(a,b).
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Old February 23rd, 2009, 07:03 PM
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Quote:
Originally Posted by 11rdc11 View Post
Thanks both my teacher at the high school and university level for some reason never thought this was important and just went directly to limits and derivatives without teaching the proofs.
Student's eye glaze over when I mention this.
Plus books are dropping it, so don't blame your professors.
All books are becoming more and more watered down.
Some schools don't even teach trig substitution and I see hyperbolics are disappearing too...
Zill's DE book used to have lots of problems with cosh and sinh and now it hardly has any.
That stuff is really handy in DE.
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Old August 17th, 2009, 04:41 PM
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If anyone is interested I have a few rigorous limit examples with animations on my web site for both epsilon-delta proofs and the epsilon-M proofs if you will for limits at infinity

Calculus 1

They are rougly in the middle of the page as I start with an intuitive approach leading up the roigorous definitions
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