0.5 0 -0.5 9(1) h(z) 1/2 X (a) Plot of g(x) and h(z). 1.5 0.5 1 0 2 -0.5 -1 0.2 0.4 X 0.6 0.8 (b) Plot of f(x)=x²-sin(4x+1/5). Consider the root-finding problem ƒ(x) = 0 with ƒ(x) := x² — sin(4x+1/5) for x € [0, 1]; see figure (b). (a) Compute one iteration of either Newton's method or secant method, your choice. If you choose Newton's method then take to = 1/2 and compute 2₁. If you choose secant method then take zo = 1/2,21 = 1 and compute 22. (b) Based on the plot of f(x), for what choice of initializations will the method you chose in part (a) not converge to the desired root? Make sure to motivate your response.
0.5 0 -0.5 9(1) h(z) 1/2 X (a) Plot of g(x) and h(z). 1.5 0.5 1 0 2 -0.5 -1 0.2 0.4 X 0.6 0.8 (b) Plot of f(x)=x²-sin(4x+1/5). Consider the root-finding problem ƒ(x) = 0 with ƒ(x) := x² — sin(4x+1/5) for x € [0, 1]; see figure (b). (a) Compute one iteration of either Newton's method or secant method, your choice. If you choose Newton's method then take to = 1/2 and compute 2₁. If you choose secant method then take zo = 1/2,21 = 1 and compute 22. (b) Based on the plot of f(x), for what choice of initializations will the method you chose in part (a) not converge to the desired root? Make sure to motivate your response.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![0.5
0
-0.5
-g(1)
h(z)
1/2
X
(a) Plot of g(x) and h(x).
1.5
0.5
0
-0.5
1
-1
2
0
0.2
0.4
X
0.6
0.8
(b) Plot of f(x) = x² = sin(4x+1/5).
1
Consider the root-finding problem ƒ(x) = 0 with f(x) := x² — sin(4x+1/5) for x = [0, 1]; see figure (b).
(a) Compute one iteration of either Newton's method or secant method, your choice.
• If you choose Newton's method then take to = 1/2 and compute 2₁.
• If you choose secant method then take xo = 1/2, 2₁ = 1 and compute 22.
(b) Based on the plot of f(x), for what choice of initializations will the method you chose in part (a)
not converge to the desired root? Make sure to motivate your response.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1dbcb96-b484-476e-adb0-126482b446f4%2F48675178-f1c2-418c-bffd-2fb1fa08f42b%2Fp5uq1tk_processed.png&w=3840&q=75)
Transcribed Image Text:0.5
0
-0.5
-g(1)
h(z)
1/2
X
(a) Plot of g(x) and h(x).
1.5
0.5
0
-0.5
1
-1
2
0
0.2
0.4
X
0.6
0.8
(b) Plot of f(x) = x² = sin(4x+1/5).
1
Consider the root-finding problem ƒ(x) = 0 with f(x) := x² — sin(4x+1/5) for x = [0, 1]; see figure (b).
(a) Compute one iteration of either Newton's method or secant method, your choice.
• If you choose Newton's method then take to = 1/2 and compute 2₁.
• If you choose secant method then take xo = 1/2, 2₁ = 1 and compute 22.
(b) Based on the plot of f(x), for what choice of initializations will the method you chose in part (a)
not converge to the desired root? Make sure to motivate your response.
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