Results 1 to 2 of 2

Math Help - Inequality

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    Inequality

    I can't prove the next inequality:

    Let a,b be in R and b>a. Prove that:

    e^b - e^a >= (b-a)*(a+b+2)/2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2008
    From
    Paris, France
    Posts
    1,174
    Quote Originally Posted by Also sprach Zarathustra View Post
    I can't prove the next inequality:

    Let a,b be in R and b>a. Prove that:

    e^b - e^a >= (b-a)*(a+b+2)/2
    You have e^b-e^a=e^{\frac{a+b}{2}}2\sinh\frac{b-a}{2}. Furthermore, e^x\geq x+1 and \sinh x\geq x (since \sinh x=\int_0^x \cosh t dt\geq \int_0^x 1 dt=x). Put these together, and you'll get your inequality.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: January 11th 2011, 08:20 PM
  2. Replies: 3
    Last Post: December 12th 2010, 01:16 PM
  3. inequality
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: July 26th 2010, 04:34 AM
  4. inequality
    Posted in the Algebra Forum
    Replies: 4
    Last Post: July 24th 2010, 12:08 PM
  5. Inequality
    Posted in the Algebra Forum
    Replies: 0
    Last Post: October 8th 2009, 03:06 AM

Search Tags


/mathhelpforum @mathhelpforum