1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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)
    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: Continuous function
  1. Continuous Functions (Replies: 2)

  2. Continuity function (Replies: 8)

  3. Continuous Functions (Replies: 11)