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13 Nov 2019
(a) Suppose f(z) is defined on the interval [0, 1] by the following rule f() is the first digit in the decimal expansion for For instance, f(0.719) 7 and f(e-1) 3. But note that some numbers have two decimal expansions. For instance, í = 0.5 0.499 and : 0.35 0.34999 . . .. In such cases, one decimal expansion ends with an infinite trail of 9's and the other terminates. We shall agree to the convention that we will always use the terminating decimal expansion. Hence f4) = 5 and f 3. i. Sketch the graph of yf( with appropriate scales for r and y. ii. Explain why y- f(x) is integrable on [0,1]. ii. Calculate the integral Jo f(x) dx. Can you use fundamental theorem of calculus?
(a) Suppose f(z) is defined on the interval [0, 1] by the following rule f() is the first digit in the decimal expansion for For instance, f(0.719) 7 and f(e-1) 3. But note that some numbers have two decimal expansions. For instance, í = 0.5 0.499 and : 0.35 0.34999 . . .. In such cases, one decimal expansion ends with an infinite trail of 9's and the other terminates. We shall agree to the convention that we will always use the terminating decimal expansion. Hence f4) = 5 and f 3. i. Sketch the graph of yf( with appropriate scales for r and y. ii. Explain why y- f(x) is integrable on [0,1]. ii. Calculate the integral Jo f(x) dx. Can you use fundamental theorem of calculus?
Reid WolffLv2
24 Apr 2019