Continuous function

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Homework Statement


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:

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