Results 1 to 4 of 4

Math Help - proof of continuity

  1. #1
    Newbie
    Joined
    Feb 2007
    Posts
    23

    proof of continuity

    A) Let f: D -> R and define |f|: D->R by |f|(x) = |f(x)|. Suppose that f is continuous at c element of D. Prove that |f| is continuous at C

    B) if |f| os cpmtomipis at c. does it follow that f is continuous at c? Justify your answer.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1
    For part A just see that: ||f(x)|-|f(c)||<|f(x)-f(c)|.

    Review part B; canít read it.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2007
    Posts
    23
    sorry, that funky word is suppose to say continuous
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1
    Consider F(x)=-1 if x<0 and F(x)=1 if x>0.
    Is |F| continuous at 0?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with a continuity proof
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: December 9th 2009, 07:49 AM
  2. Continuity proof
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: November 9th 2009, 09:34 AM
  3. Another continuity proof
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 22nd 2009, 01:36 PM
  4. Continuity proof
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: April 6th 2009, 08:57 PM
  5. Continuity proof
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 15th 2009, 02:25 PM

Search Tags


/mathhelpforum @mathhelpforum