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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)