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I Find the multiplicity of the root r = 0 of f(x) = sin³ 1 +26 - 2x¹-x³-1, and estimate the number of steps of Newton's Method to converge within six correct places (Use zo= 1). (Hint: Follow example discussed from video)

I Find the multiplicity of the root r = 0 of f(x) = sin³ 1 +26 - 2x¹-x³-1, and estimate the number of steps of Newton's Method to converge within six correct places (Use zo= 1). (Hint: Follow example discussed from video)

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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I 3. Find the multiplicity of the root r = 0 of f(x) = sin³ ¹ +16 −2¹-1³-1, and estimate the number of steps of Newton's Method to converge within six correct places (Use zo = 1). (Hint: Follow example discussed from video)
Transcribed Image Text:I 3. Find the multiplicity of the root r = 0 of f(x) = sin³ ¹ +16 −2¹-1³-1, and estimate the number of steps of Newton's Method to converge within six correct places (Use zo = 1). (Hint: Follow example discussed from video)
Expert Solution
Step 1

Finding multiplicity of the root : Consider f(x)=0 with root r. The multiplicity of a root r is m if f(r)=f'(r)=f"(r)=……………=fm-1(x)=0 and fm(r)≠0.

Newton's Method : Newton's method is a root- finding algorithm that provide a more accurate approximation to the root of a real-valued function.

Formula :    xn+1=xn-f(xn)f'(xn)

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