Use Newton's method to find the zeros of f(x) = 4x² - 4x² using the given starting values in (a) through (c).(a) xo = -1.5 and Xo = - 0.9, lying in=O A. For Xo =B. For Xo-1.5 and Xo1.5 and Xo√2(-∞, -1/2)==- 0.9, Newton's method does not converge. The values of x; alternate between 1.5 and 0.9 as i increases.==-0.9, X₁→ as i gets large.

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Answered: Use Newton's method to find the zeros…

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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2. Start with the quadratic function: f(x) = ax² +bx+c and follow the steps below. (a) Step 1: Show that f(¹) a Assume that a 0. Hint: We did something like this when solving for the quadratic roots formula. - (b) Step 2: That part of f(x) that depends on x is given by (x + b)². We want to a (x + 2)² − b ² + € a study exactly how (x + 2)² depends upon x. Show that: i. (x + 2)² ≥ 0 for all values of 2a b 2a ii. (x + 2)² = 0 only when x = 2a to iii. This is an interesting result. Suppose that h is a positive number, it can be large of small. Show that (x + 2)² takes the value h² when x = h. Using a b +h. 2a 2a b Next show that (x + 2)² takes the value h² when x = diagram show that this means that (x + 2)² is symmetric about x = - It behaves just like the function x² and we know x² is symmetric about x = 0. b 2a iv. Now, - X=- b so (x + 2)² = 0 has 2 identical roots equal 2a b can be positive, negative or zero. So, we can conclude that if 2a 2a 2a = 0 then (x + 2)² behaves exactly like…
LETTER C ONLY. DO NOT ROUND OFF
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