find a function that is cont. in a interval that is non-closed but is bounded where f(x) is not bounded? Also find a function f, that is cont. in a closed non-bounded interval, s.t. f(x) is not bounded.
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For the first, can you find a non-closed, bounded interval on which $f(x)=\frac1x$ is unbounded? For the second, remember that $[0,\to)$, the set of non-negative real numbers, is a closed interval that isn’t bounded; I’ll bet that you can find a continuous, unbounded function on it.