Let p be the unique root of x^5 + 4x − 11 = 0 in the interval [a1, b1] = [1, 2], and pn be the midpoint of the interval [an, bn] used for the nth bisection. How large should n be to ensure that |pn − p| < 10^−14 according to the error estimate for the Bisection Method?

Let p be the unique root of x^5 + 4x − 11 = 0 in the interval [a1, b1] = [1, 2], and pn be the midpoint of the interval [an, bn] used for the nth bisection. How large should n be to ensure that |pn − p| < 10^−14 according to the error estimate for the Bisection Method?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let p be the unique root of x^5 + 4x − 11 = 0 in the interval [a1, b1] = [1, 2],
and pn be the midpoint of the interval [an, bn] used for the nth bisection. How large should n be to ensure that |pn − p| < 10^−14 according to the error estimate for the Bisection Method?

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