Results 1 to 3 of 3

Math Help - Help on Hint

  1. #1
    Member mabruka's Avatar
    Joined
    Jan 2010
    From
    Mexico City
    Posts
    150

    Help on Hint

    hi I need some help understanding the hint this exercise gives:




    Where  I=[-2,2] and
    A_1=\{x \in I :  Q_c(x)\in I \}.

    p_+ is the fixed point of Q_c in  [0,2].

    p_+=\frac{1+ \sqrt{1-4c}}{2}


    I dont understand why it suffices to find the c-values the hint points to guarantee the conclusion for x \in [0,\frac{1}{2}]

    thank you!
    Last edited by mabruka; February 21st 2010 at 07:12 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by mabruka View Post
    hi I need some help understanding the hint this exercise gives:




    Where  I=[-2,2] and
    A_1=\{x \in I : Q_c(x)\in I \}.

    p_+ is the fixed point of Q_c in  [0,2].

    p_+=\frac{1+ \sqrt{1-4c}}{2}


    I dont understand why it suffices to find the c-values the hint points to guarantee the conclusion for x \in [0,\frac{1}{2}]

    thank you!

    Something seems to be missing in the question

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member mabruka's Avatar
    Joined
    Jan 2010
    From
    Mexico City
    Posts
    150
    hmm ok.


    We need to prove that |Q^{\prime}_c(x)| > 1 for all x \ in [-2,2].


    It is easy to see that it is true for x  > \frac{1}{2}

    To prove it for   x \leq \frac{1}{2} it is suggested to investigate which values of c
    satisfy:

    Q_c(\frac{1}{2})< -p_+

    My question is:
    Why it suffices to find the values of c which satisfy Q_c(\frac{1}{2})< -p_+ to show that |Q^{\prime}_c(x)| > 1 for x  \leq \frac{1}{2} ?

    In other words, why does the hint "works" ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integral of x.arctan(x) with hint with hint
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 22nd 2010, 06:57 AM
  2. Please give me a hint on how to solve this?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 25th 2009, 06:22 AM
  3. Induction hint
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: February 6th 2008, 07:00 PM
  4. Integral hint
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 23rd 2008, 01:42 PM
  5. A Hint needed...stuck
    Posted in the Geometry Forum
    Replies: 2
    Last Post: September 24th 2006, 01:07 AM

Search Tags


/mathhelpforum @mathhelpforum