Results 1 to 3 of 3

Thread: eplison delta proof problem

  1. #1
    Senior Member
    Joined
    May 2012
    From
    Toronto
    Posts
    274
    Thanks
    1

    eplison delta proof problem

    eplison delta proof problem-screen-shot-2012-10-23-10.40.19-am.png

    Somehow the methodology never makes sense to me.

    I understand the idea behind it, but I never understand how one chooses the appropriate number for epsilon. Can someone break down how one would do this problem?

    thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    20,420
    Thanks
    2306
    Awards
    1

    Re: eplison delta proof problem

    Quote Originally Posted by kingsolomonsgrave View Post
    Click image for larger version. 

Name:	Screen Shot 2012-10-23 at 10.40.19 AM.png 
Views:	4 
Size:	14.4 KB 
ID:	25363
    Somehow the methodology never makes sense to me.
    I understand the idea behind it, but I never understand how one chooses the appropriate number for epsilon.
    The fact is you do not choose the epsilon. That is given at the start of the process.
    Your task is to a delta that makes it all work out.
    So you control delta, in this case the size of |x-3|.
    Look at \left| {\frac{{2x + 4}}{5} - 2} \right| = \left| {\frac{{2x - 6}}{5}} \right| = \frac{2}{5}\left| {x - 3} \right|.
    Ah, there is that factor you control. To get \frac{2}{5}\left| {x - 3} \right|<\varepsilon we pick \delta=\frac{5\varepsilon}{2}
    Last edited by Plato; Oct 23rd 2012 at 08:21 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Mar 2010
    Posts
    1,021
    Thanks
    263

    Re: eplison delta proof problem

    Right - you're given \epsilon and you need to find a \delta (which will be a function of \epsilon) that works. So you're doing the algebra backwards. Then when you write your proof, doing the algebra forward, it works. There's an excellent paper on how to do these proofs right here on the MHF Calculus forum - it's one of the "sticky" threads at the top.

    - Hollywood
    Last edited by hollywood; Oct 23rd 2012 at 11:30 AM. Reason: grammar
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 15
    Last Post: Jun 8th 2011, 12:13 PM
  2. eplison lambda limit proof
    Posted in the Calculus Forum
    Replies: 0
    Last Post: Nov 7th 2010, 02:48 PM
  3. Replies: 11
    Last Post: Jan 14th 2010, 07:24 PM
  4. Replies: 0
    Last Post: Oct 27th 2009, 08:06 AM
  5. epsilon-delta proof
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Oct 26th 2009, 08:28 PM

Search Tags


/mathhelpforum @mathhelpforum