Results 1 to 3 of 3

Thread: Unique resolution

  1. #1
    Super Member dhiab's Avatar
    Joined
    May 2009
    From
    ALGERIA
    Posts
    582
    Thanks
    3

    Unique resolution

    Prove that equation , accepts an unique resolution : and :
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    5
    Quote Originally Posted by dhiab View Post
    Prove that equation , accepts an unique resolution : and :
    put $\displaystyle g(x)=f(x)-x$, then:

    $\displaystyle g'(x)=(-2x^2+x+3)e^{-x}-1$

    Now look at $\displaystyle -2x^2+x+3$ this has roots at $\displaystyle x=-1$ and $\displaystyle 3/2$, so $\displaystyle -2x^2+x+3$ has constant sign for $\displaystyle x>3/2$, a quick check shows that this is negative. Hence $\displaystyle g'(x)<0$ for $\displaystyle x>3/2$

    Thus $\displaystyle g(x)$ is decreasing when $\displaystyle x>3/2$. To complete the proof it remains to show that $\displaystyle g(3/2)$ is positive and $\displaystyle g(2)$ is negative.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member dhiab's Avatar
    Joined
    May 2009
    From
    ALGERIA
    Posts
    582
    Thanks
    3
    Hello captain thank you for your resolution Ajout : alpha = 1.91 and g(1.5)=0.5 , g(2)=-0.12
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Resolution
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: Nov 6th 2011, 06:14 PM
  2. Resolution with unification
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: May 29th 2011, 04:11 PM
  3. resolution of vectors
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: Sep 20th 2009, 04:34 PM
  4. projective resolution
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 21st 2009, 01:52 AM
  5. Free resolution
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: Feb 19th 2009, 02:50 PM

Search Tags


/mathhelpforum @mathhelpforum