The function is unbounded on the closed interval. How to prove that there is a point in this interval that makes the function unbounded in the domain of this point by compactness theorem?

It is proved that the function is unbounded in the closed interval. If f(x) is unbounded in [a, b], then at least ξ of any m belongs to [a, b].

make | f(ξ)| & gt； m，

Bounded sequences must contain convergent subsequences, then {xn} exists in [a, b] so that.

lim(xn)=ξn-& gt； Infinite; unbordered

F(x) can be unbounded in the field of ξ.

There is less writing on it, and it is not easy to write something. You can refer to mathematical analysis and have similar conclusions to prove it. Please forgive me if there is anything wrong!

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