4. Let f(x) x² + cos(Tr). f&)= Qx -Tsin(Tx) (a) Use Newton's method to find the root of f(x) with x1 =-1/2 and within a tolerance of 10-4 (b) Use Newton's method to find the root of f(x) with x1 = 3 and within a tolerance of 10-4. (c) Explain why Newton's method fails with an initial guess of x1 =0.
4. Let f(x) x² + cos(Tr). f&)= Qx -Tsin(Tx) (a) Use Newton's method to find the root of f(x) with x1 =-1/2 and within a tolerance of 10-4 (b) Use Newton's method to find the root of f(x) with x1 = 3 and within a tolerance of 10-4. (c) Explain why Newton's method fails with an initial guess of x1 =0.
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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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Please solve A,B, and C
![## Problem 4
Let \( f(x) = x^2 + \cos(\pi x) \).
The derivative is given by:
\[ f'(x) = 2x - \pi \sin(\pi x) \].
### Tasks
#### (a)
Use Newton's method to find the root of \( f(x) \) with an initial guess of \( x_1 = -1/2 \) and within a tolerance of \( 10^{-4} \).
#### (b)
Use Newton's method to find the root of \( f(x) \) with an initial guess of \( x_1 = 3 \) and within a tolerance of \( 10^{-4} \).
#### (c)
Explain why Newton's method fails with an initial guess of \( x_1 = 0 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2107c9d4-03cf-46c4-aa9a-f455311ac0bc%2F3017e0fd-3680-4582-a334-097dc7025518%2Fx5r6qqq.jpeg&w=3840&q=75)
Transcribed Image Text:## Problem 4
Let \( f(x) = x^2 + \cos(\pi x) \).
The derivative is given by:
\[ f'(x) = 2x - \pi \sin(\pi x) \].
### Tasks
#### (a)
Use Newton's method to find the root of \( f(x) \) with an initial guess of \( x_1 = -1/2 \) and within a tolerance of \( 10^{-4} \).
#### (b)
Use Newton's method to find the root of \( f(x) \) with an initial guess of \( x_1 = 3 \) and within a tolerance of \( 10^{-4} \).
#### (c)
Explain why Newton's method fails with an initial guess of \( x_1 = 0 \).
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