EE 221 Assignment 04 (Root finding) 1/2 Guidelines: For paper problems, start each problem on a new sheet of paper. Write on only one side of each sheet. Clearly write your name, the assignment number and the problem number in the upper-right corner of each sheet. Staple all sheets together. For the coding problems, place all programs in a directory named FullNameHW04 - zip it and upload to the appropriate drop box. FullName refers to your full name (e.g., JaneDoeHW04.zip). Problem 1 (paper) Using a calculator, pencil and paper, apply the bisection method to find a root of y=f(x)=1-2xcos.x by filling in a table of the form shown below. For the “sign" columns enter + or – sign f (a) sign f (x) b. sign f (b) a 0.5 0.7 In each row x=(a+b)/2. Once the table is complete, report your best estimate of the root in the form rtd.
EE 221 Assignment 04 (Root finding) 1/2 Guidelines: For paper problems, start each problem on a new sheet of paper. Write on only one side of each sheet. Clearly write your name, the assignment number and the problem number in the upper-right corner of each sheet. Staple all sheets together. For the coding problems, place all programs in a directory named FullNameHW04 - zip it and upload to the appropriate drop box. FullName refers to your full name (e.g., JaneDoeHW04.zip). Problem 1 (paper) Using a calculator, pencil and paper, apply the bisection method to find a root of y=f(x)=1-2xcos.x by filling in a table of the form shown below. For the “sign" columns enter + or – sign f (a) sign f (x) b. sign f (b) a 0.5 0.7 In each row x=(a+b)/2. Once the table is complete, report your best estimate of the root in the form rtd.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![**EE 221 Assignment 04 (Root Finding)**
**Guidelines**: For paper problems, start each problem on a new sheet of paper. Write on only one side of each sheet. Clearly write your name, the assignment number, and the problem number in the upper-right corner of each sheet. Staple all sheets together. For coding problems, place all programs in a directory named FullNameHW04 - zip it and upload to the appropriate drop box. FullName refers to your full name (e.g., JaneDoeHW04.zip).
### Problem 1 (paper)
Using a calculator, pencil, and paper, apply the bisection method to find a root of
\[ y = f(x) = 1 - 2 \cos x \]
by filling in a table of the form shown below. For the “sign \( f(a) \)” and “sign \( f(b) \)” columns enter \( + \) or \( - \).
| \( a \) | sign \( f(a) \) | \( x \) | sign \( f(x) \) | \( b \) | sign \( f(b) \) |
|--------|-----------------|---------|-----------------|---------|-----------------|
| 0.5 | | | | 0.7 | |
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
In each row \( x = (a + b) / 2 \). Once the table is complete, report your best estimate of the root in the form \( r \pm \delta \).
### Problem 2 (paper)
(a) For the function \( f(x) = 1 - 2 \cos x = 0 \) write out the explicit form of the Newton's method iteration formula](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5312a15-860e-407c-ae9e-8729c86c8316%2F3c84a86e-ce42-4af2-bddd-a760b292d290%2Fqmnn8hn_processed.png&w=3840&q=75)
Transcribed Image Text:**EE 221 Assignment 04 (Root Finding)**
**Guidelines**: For paper problems, start each problem on a new sheet of paper. Write on only one side of each sheet. Clearly write your name, the assignment number, and the problem number in the upper-right corner of each sheet. Staple all sheets together. For coding problems, place all programs in a directory named FullNameHW04 - zip it and upload to the appropriate drop box. FullName refers to your full name (e.g., JaneDoeHW04.zip).
### Problem 1 (paper)
Using a calculator, pencil, and paper, apply the bisection method to find a root of
\[ y = f(x) = 1 - 2 \cos x \]
by filling in a table of the form shown below. For the “sign \( f(a) \)” and “sign \( f(b) \)” columns enter \( + \) or \( - \).
| \( a \) | sign \( f(a) \) | \( x \) | sign \( f(x) \) | \( b \) | sign \( f(b) \) |
|--------|-----------------|---------|-----------------|---------|-----------------|
| 0.5 | | | | 0.7 | |
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
In each row \( x = (a + b) / 2 \). Once the table is complete, report your best estimate of the root in the form \( r \pm \delta \).
### Problem 2 (paper)
(a) For the function \( f(x) = 1 - 2 \cos x = 0 \) write out the explicit form of the Newton's method iteration formula
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