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.
Brian M. Scott
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for the first (0,1) and the second log(x).thank you! – Klara Oct 18 '12 at 04:33
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@Klara: You’re welcome! (For the second you could even just use $f(x)=x$; they don’t come much simpler!) – Brian M. Scott Oct 18 '12 at 04:34
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true y=x works just as well. Thank you again! – Klara Oct 18 '12 at 04:36