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Exercise 3: Consider the function: 17 f(x) = x4 - 2r2 16 Prove that it has a positive root, and a negative root. Show that the Newton-Rhapson method with an initial guess of xo = 1/2 fails to converge to the positive root. Choose a different initial guess, and estimtae the positive root to four decimal places.

Exercise 3: Consider the function: 17 f(x) = x4 - 2r2 16 Prove that it has a positive root, and a negative root. Show that the Newton-Rhapson method with an initial guess of xo = 1/2 fails to converge to the positive root. Choose a different initial guess, and estimtae the positive root to four decimal places.

Advanced Engineering Mathematics
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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Exercise 3: Consider the function: 17 f(x) = x4 - 2r2 16 Prove that it has a positive root, and a negative root. Show that the Newton-Rhapson method with an initial guess of xo = 1/2 fails to converge to the positive root. Choose a different initial guess, and estimtae the positive root to four decimal places.
Transcribed Image Text:Exercise 3: Consider the function: 17 f(x) = x4 - 2r2 16 Prove that it has a positive root, and a negative root. Show that the Newton-Rhapson method with an initial guess of xo = 1/2 fails to converge to the positive root. Choose a different initial guess, and estimtae the positive root to four decimal places.
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