Results 1 to 6 of 6

Math Help - function bounded on an interval?

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    26

    function bounded on an interval?

    we have a function
    f(x) = x^2 - 3 for x<2, 6/x for x>=2 (x greater or equal to 2)

    i've shown that the limits of this function from the left and right of 2 respectively are 1 and 3. (given in qn)

    also shown that *if any function is continuous on [a,b] then it is bounded on [a,b]*

    now i need to find out whether i can
    1) use the above theorem (in bold) to the function f(x) on the interval [0,5]

    2) determine whether f(x) is bounded on [0,5]

    -----------------------------------------------------------
    my thoughts - clearly the function isn't continuous at 2, but it is piecewise continuous on the interval, so.... it's okay to use the theorem? or does it have to be continuous everywhere?


    apologies for the lack of latex
    thank youuu
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    Re: function bounded on an interval?

    Quote Originally Posted by cassius View Post

    also shown that *if any function is continuous on [a,b] then it is bounded on [a,b]*


    apologies for the lack of latex
    thank youuu
    It is Weierstrass first theorem.(from Hebrew)

    Extreme value theorem - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,790
    Thanks
    1687
    Awards
    1

    Re: function bounded on an interval?

    Quote Originally Posted by cassius View Post
    we have a function
    f(x) = x^2 - 3 for x<2, 6/x for x>=2 (x greater or equal to 2
    also shown that *if any function is continuous on [a,b] then it is bounded on [a,b]*
    now i need to find out whether i can
    1) use the above theorem (in bold) to the function f(x) on the interval [0,5]

    2) determine whether f(x) is bounded on [0,5]
    1) Because f is not continuous on [0,5] you cannot use that theorem.

    2) But you can prove it is bounded there any simple inequalities.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Apr 2010
    Posts
    26

    Re: function bounded on an interval?

    if we draw the graph of f(x) we can see it is bounded below by -3 at x=0; is this correct?
    thank you
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,790
    Thanks
    1687
    Awards
    1

    Re: function bounded on an interval?

    Quote Originally Posted by cassius View Post
    if we draw the graph of f(x) we can see it is bounded below by -3 at x=0; is this correct?
    -3\le f(x)\le 3 if x\in [0,5]
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Apr 2010
    Posts
    26

    Re: function bounded on an interval?

    ah, ja thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: April 3rd 2011, 05:30 AM
  2. Replies: 3
    Last Post: March 17th 2010, 06:12 PM
  3. Replies: 3
    Last Post: April 16th 2009, 03:09 PM
  4. Replies: 1
    Last Post: February 7th 2009, 06:38 AM
  5. continuous on closed and bounded interval
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 13th 2007, 08:59 AM

Search Tags


/mathhelpforum @mathhelpforum