Results 1 to 5 of 5

Math Help - Mean Value Theorem proof

  1. #1
    Junior Member
    Joined
    Mar 2010
    Posts
    45

    Mean Value Theorem proof

    Could someone prove this by the mean value theorem:
    -ln(1-x) < x/(1-x) for 0 < x< 1

    I got really close to it..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,712
    Thanks
    1641
    Awards
    1
    Use the mean value to prove Napierís inequality: if 0<a<b then \frac{1}{b}\le\frac{\ln(b)-\ln(a)}{b-a}\le\frac{1}{a}.
    Then let a=1-x~\&~b=1.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2010
    Posts
    45
    why do you let a=1-x? not a=x
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,712
    Thanks
    1641
    Awards
    1
    Quote Originally Posted by Monster32432421 View Post
    why do you let a=1-x? not a=x
    Because a=1-x gives us what we want.
    But a=x does not.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jan 2010
    Posts
    133
    (Already seen 2 posters posting the same question, interesting)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Mean Value Theorem Proof
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 26th 2010, 09:16 AM
  2. Proof of theorem...
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 31st 2010, 02:40 PM
  3. proof using mean value theorem
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 15th 2009, 02:24 PM
  4. Proof using Mean Value Theorem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 19th 2008, 04:16 AM
  5. proof of a theorem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 4th 2008, 06:36 PM

Search Tags


/mathhelpforum @mathhelpforum