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Continuity of Functions

Continuity of Functions

Example 1

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

Example 2

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

Example 3

Does a function f 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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