Results 1 to 3 of 3

Math Help - Difficult epsilon proof question

  1. #1
    Member
    Joined
    Jan 2010
    Posts
    232

    Difficult epsilon proof question

    Once again, the textbook from which this question comes from has no prior example which I could reference to even possibly answer this.

    If \epsilon>0, show that |2x^2-6xy+5y^2|<\epsilon when (x^2+y^2)^{1/2}<(\epsilon/13)^{1/2}.

    My Prof. is a true sadist...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Jan 2010
    Posts
    232
    Through other online sources, I've come up with this so far. I suspect, however, that it has some pieces missing.

    If we square (x^2+y^2)^{1/2}<(\epsilon/13)^{1/2}, we get x^2+y^2<\epsilon/13.
    This says that (x,y) lies inside a circle of radius \sqrt{\epsilon/13} around the origin.
    Using the triangle inequality, (which is |a+b|\leq|a|+|b|)
    |2x^2-6xy+5y^2|\leq |2x^2|+|6xy|+|5y^2|
    The condition x^2+y^2<\epsilon/13 means that separately, x^2, y^2 and |xy| are all less than \epsilon/13.
    Therefore, |2x^2|+|6xy|+|5y^2|<(2+6+5)(\epsilon/13).

    If there are any errors in this, I'd appreciate it if they were pointed out.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,417
    Thanks
    718
    Seems correct to me.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Epsilon - Delta Proof Question
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 10th 2011, 06:31 PM
  2. Replies: 15
    Last Post: June 8th 2011, 11:13 AM
  3. Question regarding above epsilon-delta proof
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 27th 2010, 11:38 AM
  4. Solving Delta Epsilon Proof (Given Epsilon)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 15th 2010, 03:42 PM
  5. Epsilon delta proof
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 6th 2010, 05:35 PM

Search Tags


/mathhelpforum @mathhelpforum