Results 1 to 4 of 4

Math Help - example of a continuous funtion where the sup is not achieved

  1. #1
    Member
    Joined
    Apr 2010
    Posts
    133

    example of a continuous funtion where the sup is not achieved

    Also, if we let a and b be real number with a<b then what is an example of a bounded f on [a,b] for which sup_[a,b] f is not achieved?

    What would be an example of a bounded, continuous f on [a, \infty) for which sup_[a, \infty) f is not achieved?

    and what would be an example of a bounded, continuous f on [a,b) for which sup_[a,b) f is not achieved?

    For the first one would it be : f(x)= { x, a<=x<=b
    0, x=b}
    second, f(x)= -1/x+1

    third, f(x)=x ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Aug 2009
    From
    Israel
    Posts
    976
    For the first one you need a strong inequality sign with b (f(x) = x for a<=x<b); for the second, what happens if a = -1? Only a slight change is required..
    Third is correct.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Apr 2010
    Posts
    133
    Quote Originally Posted by Defunkt View Post
    For the first one you need a strong inequality sign with b (f(x) = x for a<=x<b); for the second, what happens if a = -1? Only a slight change is required..
    Third is correct.
    hm, would i use absolute value signs?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Aug 2009
    From
    Israel
    Posts
    976
    Quote Originally Posted by alice8675309 View Post
    hm, would i use absolute value signs?
    That works. You can also use \frac{-1}{x-a-1}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Norm could be achieved f=1?
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 23rd 2010, 07:31 AM
  2. Compactness; show inf is achieved
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: February 23rd 2010, 04:02 PM
  3. A Funtion of 3 uniform, continuous random variables
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: March 27th 2009, 08:26 AM
  4. Funtion bessel
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 2nd 2008, 07:01 AM
  5. Polynomial Funtion HELP PLEASE!!!
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: October 13th 2007, 01:11 PM

Search Tags


/mathhelpforum @mathhelpforum