Let (x) = x 2 and let RN, LN, and MN be the approximations for the interval

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Let ƒ(x) = xand let RN, LN, and MN be the approximations for the interval [0, 1]. Show that

LN 3 1 2N 1 6N 1 3 12N MN 31

Then, given that the area under the graph of y = xover [0, 1] is 1/3, rank the three approximations RN, LN, and MN in order of increasing accuracy (use Exercise 74).


Data From Exercise 74

Let ƒ(x) = xand let RN, LN, and MN be the approximations for the interval [0, 1].

Show that RN = - 1 1 + 3 2N + 1 6N 1 Interpret the quantity + 2N 1 6N as the area of a region.


Data From Exercise 74

Let ƒ(x) = xand let RN, LN, and MN be the approximations for the interval [0, 1].

Show that RN = - 1 1 + 3 2N + 1 6N 1 Interpret the quantity + 2N 1 6N as the area of a region.

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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