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Math Help - Epsilon-N

  1. #1
    Junior Member
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    Epsilon-N

    See Q6 on attached document....

    Part (a) is just a definition and is simple enough.

    Part (b) i got an answer 10/64 \epsilon using the "big top/small bottom" technique. Was this the right way to do it?

    Part (c) i have no idea how to tackle these types of questions so was hoping someone would be able to walk me through the theory for them.

    Thanks
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  2. #2
    Senior Member
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    I'm not sure your answer for part (b) is right. How did you obtain it? I got N=\frac{1}{2\epsilon }.

    Part (c) is easy enough:

    (i) |a_n-a|<a/2 \leftrightarrow -a/2 < a_n-a <a/2. Now add a to both sides.

    (ii) This is just using the difference of two squares:

    |a_n-a| = |(\sqrt a_n -\sqrt a)(\sqrt a_n+\sqrt a)|

    From (i) we have that \sqrt a_n > \sqrt{a/2} and so \sqrt a_n +\sqrt a> \sqrt{a/2} + \sqrt a . and the result follows (I think \le is a typo).

    Part (c) is needed for part (d).
    Last edited by ojones; May 13th 2010 at 11:07 PM.
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