# Boundedness Exercises

### Example 1

- Does a function that is bounded on [
*a*,*b*] need to be continuous on [*a*,*b*]? Why or why not?

### Example 2

Does a function that is continuous on an open interval (*a*, *b*) need to be bounded on that interval?

### Example 3

Does a function that is discontinuous on a closed interval [*a*, *b*] need to be bounded on that interval?

### Example 4

Let . For each given function and interval, determine if we can use the Boundedness Theorem to conclude the function is bounded on that interval. If not, explain why not.

- [0, 5]

- (0, 5)

- (2, 3)

- [0, 1]

- [0, 2)

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