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Continuous function

  1. May 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Do the graphic rendering (and write the full proof) of the function h : [0,1) -> [tex]\Re[/tex] , which is continuous and bounded but does not reach it's bounds.

    2. The attempt at a solution
    If h is continuous : exists
    lim h(x) = h(x0)
    x->xo
    If h is bounded:
    А ≤ h(x) ≤ В for every x[tex]\in[/tex][0, 1)

    I thought that the function f(x) = [tex]\frac{sin\frac{1}{1-x}}{2-x}[/tex]
    works but I can't quite do the proof and the graphic rendering which leads me to the point that I'm wrong. Pls help :confused:
    f(x) = [tex]\frac{sin\frac{1}{1-x}}{2-x}[/tex] 's graphic rendering :
    View attachment untitled.bmp
    is this right?!
     
    Last edited: May 9, 2009
  2. jcsd
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