Results 1 to 2 of 2

Math Help - derivatives

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    17

    derivatives

    I can not figure this problem out. Please somebody help me. let f: (a,b) \rightarrowR, where a,b \inR be a function and let x \in(a,b). Prove that if limh \rightarrow0|f(x+h)-f(x)|=0, then lim h \rightarrow0|f(x+h)-f(x-h)| = 0.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Deadstar's Avatar
    Joined
    Oct 2007
    Posts
    722
    I believe it's along the lines of...

    \lim_{h \to 0} |f(x+h) - f(x-h)|

    = \lim_{h \to 0} |f(x+h) - f(x) + f(x) - f(x-h)|

    \leq \lim_{h \to 0} |f(x+h) - f(x)| + \lim_{h \to 0} |f(x) - f(x-h)| \to 0+0 = 0 \textrm{ as } h \to 0 where we used the triangle inequality in this step.

    You might need to make it a bit more rigorous but I think this is what you have to do...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivatives and Anti-Derivatives
    Posted in the Calculus Forum
    Replies: 7
    Last Post: February 6th 2011, 06:21 AM
  2. Replies: 1
    Last Post: July 19th 2010, 04:09 PM
  3. Replies: 4
    Last Post: February 10th 2009, 09:54 PM
  4. Trig derivatives/anti-derivatives
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 10th 2009, 01:34 PM
  5. Second derivatives
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 3rd 2008, 02:09 PM

Search Tags


/mathhelpforum @mathhelpforum