5. Consider the problem of taking the zeros of the the polynomial P(x) = ³x² - 6x over (2, 4). Below is an algorithm that may be used to numerically determine a zero. ²-1²-6 A: In+1 = In - 3r²-2-6* (a) Consider zo = 7. Numerically determine the value on which the sequence converges to Write the first 5 approximations of the algorithm. (b) By numerical means, estimate the order a and asymptotic error constant A of the sequence. (c) Provide an analytic proof for your claims in (c).

5. Consider the problem of taking the zeros of the the polynomial P(x) = ³x² - 6x over (2, 4). Below is an algorithm that may be used to numerically determine a zero. ²-1²-6 A: In+1 = In - 3r²-2-6* (a) Consider zo = 7. Numerically determine the value on which the sequence converges to Write the first 5 approximations of the algorithm. (b) By numerical means, estimate the order a and asymptotic error constant A of the sequence. (c) Provide an analytic proof for your claims in (c).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 92E

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