Let . For each interval, determine if we can use the Boundedness Theorem to conclude that *f* must be bounded on that interval. If not, explain why not. | |

- [0,1] - We cannot use the Boundedness Theorem, because one of the assumptions fails:
*f* is not continuous on the interval [0,1].
- [1,2] - We can use the Boundedness Theorem to conclude that
*f* is bounded on [1,2] because *f* is continuous on [1,2] and this interval is closed.
- (0,1) - We cannot use the Boundedness Theorem, because this interval is not closed.
- (0,1] - We cannot use the Boundedness Theorem, because this interval is not closed.
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