# Continuous function

## Homework Statement

Do the graphic rendering (and write the full proof) of the function h : [0,1) -> $$\Re$$ , 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$$\in$$[0, 1)

I thought that the function f(x) = $$\frac{sin\frac{1}{1-x}}{2-x}$$
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
f(x) = $$\frac{sin\frac{1}{1-x}}{2-x}$$ 's graphic rendering :
View attachment untitled.bmp
is this right?!

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