Results 1 to 8 of 8

Math Help - how to show that the following equality holds.

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    london
    Posts
    17

    how to show that the following equality holds.

    Show that f(x) is the derivative of f(.) at x if and only if lim_{h \to 0} \sup_{|t|\leqslant h} \frac{|f(x+t)-f(x)-tf^{'} (x)|}{h} = 0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,612
    Thanks
    591

    Re: how to show that the following equality holds.

    Hey ujgilani.

    Have you considered the triangle inequality?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2012
    From
    london
    Posts
    17

    Re: how to show that the following equality holds.

    Hi, thanks for your reply
    no I didn't try doing it with triangle inequality. could you please brief a little bit more.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,612
    Thanks
    591

    Re: how to show that the following equality holds.

    Basically the triangle inequality says |a+b| <= |a| + |b| where |.| is some norm.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2012
    From
    london
    Posts
    17

    Re: how to show that the following equality holds.

    yeah i know the "triangle inequality" concept but question is how we can apply it here
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,612
    Thanks
    591

    Re: how to show that the following equality holds.

    Show that |a| + |b| = 0.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Oct 2012
    From
    london
    Posts
    17

    Re: how to show that the following equality holds.

    sorry no idea how to use it in this setup
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,612
    Thanks
    591

    Re: how to show that the following equality holds.

    I think I may have given you the wrong advice: I'm thinking that since h > 0 (limit approached from the right) then |h| = h so you can put the h inside the absolute value sign. I'm sorry about the wrong advice.

    Now one approach I am thinking of is to find a situation when you can interchange the limit signs within the absolute value from outside. I do know there are theorems that gaurantee when you can do this in some situations like this:

    http://www.math.cuhk.edu.hk/course/1...onvergence.pdf
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. how to show the following equality holds.
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: October 27th 2012, 08:55 AM
  2. Replies: 3
    Last Post: March 31st 2012, 08:11 AM
  3. Replies: 2
    Last Post: September 29th 2010, 12:58 PM
  4. show the equality
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 7th 2010, 11:56 PM
  5. Show equality by combinational argument
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: September 30th 2009, 05:46 PM

Search Tags


/mathhelpforum @mathhelpforum