Let I(x) := l/x for x E (0,1] and 1(0) := 0; then I is continuous except at x = O.Show

Chapter 10, Problem 9

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Let I(x) := l/x for x E (0,1] and 1(0) := 0; then I is continuous except at x = O.Show thatI does not belong to R*[O, 1]. [Hint: Compare I with sn(x) := 1 on (1/2,1], sn(x) := 2 on(1/3,1/2], sn(x) := 3 on (1/4,1/3]"", sn(x) := n on [0, l/n].]

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