http://www.math.caltech.edu/classes/ma1a/Fa07Ma1aHW2.pdf [Broken](adsbygoogle = window.adsbygoogle || []).push({});

Problem 2

(note, I'm not a Caltech student, so this is not a violation of the Honor Code - also, solutions have been posted)

The solution to problem 2 is at

http://www.math.caltech.edu/classes/ma1a/07Ma1aSol2.pdf [Broken]

The question with the solution, how is this epsilon constructed? It seems to come out of nowhere. I tried constructing an epsilon myself.

This is what I tried:

"the question I asked was "how in the hell did the person get N? Clearly, one can do it by expressing n in terms of epsilon, but if you do that, you merely get n = (epsilon+1)^1/3 / (1 - (epsilon + 1)^1/3). of course, this > 1 / (1 - (epsilon + 1)^1/3. (and the (epsilon + 1) should not be dif. from the (epsilon - 1) in computations since the inequality reverses (and that should give you an constant dependent on epsilon that n must be bigger than.

So is the only step you have to take to express n in terms of epsilon, and then to find a value of n that is strictly less than that to ensure that the limit of the function is always less than epsilon as n -> infinity?

The question is - is the constant of the official solution better than the constant I gave?

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# Homework Help: Question on the construction of a limit

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