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Given the function: f: (0,1) => (2x+1,4x)

  1. Apr 15, 2010 #1
    Given the function: f: (0,1) => (2x+1,4x) ,find sup{[tex]||f(x)||_{E}[/tex] :xε(0,1)}

    where "E" is for Euclidean norm
     
  2. jcsd
  3. Apr 15, 2010 #2

    LCKurtz

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    Re: supremum

    What exactly are you stuck on? It looks pretty straightforward...
     
  4. Apr 15, 2010 #3
    Re: supremum

    What do you get for the supremum?
     
  5. Apr 15, 2010 #4

    LCKurtz

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    Re: supremum

    What did you get? The idea here is for you to show us what you have done and we will help you over any trouble spots or verify your work.
     
  6. Apr 15, 2010 #5
    Re: supremum

    I get 6,is it right or wrong??
     
  7. Apr 15, 2010 #6

    LCKurtz

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    Re: supremum

    Wrong.
     
  8. Apr 15, 2010 #7
    Re: supremum

    Is it not {[tex]||f(x)||_{E}[/tex] :xε(0,1)} =(0,6)??
     
  9. Apr 15, 2010 #8

    LCKurtz

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    Re: supremum

    No, it isn't. Why don't you show us your work so we can help you find your mistake.
     
  10. Apr 16, 2010 #9
    Re: supremum


    Sorry,mistake, it should be : (0,5) instead (0,6) and hence the supremum is 5
     
  11. Apr 16, 2010 #10

    HallsofIvy

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    Re: supremum

    What should be "(0, 5)"???

    It looks obvious to me that both components are increasing functions of x and that, as x approaches 1, (2x+1, 4x) approaches (3, 4).
     
  12. Apr 16, 2010 #11
    Re: supremum

    you are making a mistake read the original post again
     
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