TABLE OF CONTENTS
No. A function can be bounded on [a,b] but discontinuous on [a,b]. Here's an example:
Does a function f that is continuous on an open interval (a,b) need to be bounded on that interval?
No. Here's an example:
Does a function f that is discontinuous on a closed interval [a,b] need to be bounded on that interval?
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.