Question

prove that the bounded function in a closed interval is not continuous in that interval​

Answer 1

Answer:

A continuous function on a closed bounded interval is bounded and attains its bounds. Suppose f is defined and continuous at every point of the interval [a, b]. ... The proof that f is bounded below is similar. To show that f attains its bounds, take M to be the least upper bound of the set X = { f (x) | x ∈ [a, b] }

Answer 2

Answer:

A continuous function on a closed bounded interval is bounded and attains its bounds. Suppose f is defined and continuous at every point of the interval [a, b]. ... The proof that f is bounded below is similar. To show that f attains its bounds, take M to be the least upper bound of the set X = { f (x) | x ∈ [a, b] }.

Step-by-step explanation:

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