Using the MATLAB code f=inline('x^3 - x^2 -18'); df=inline('3*x^2 - 2*x'); ea=100; count=0; xi=0.5; while (ea>.01); count = count + 13; xil = xi - f(xi)/df(xi); ea = 100*abs(xil-xi)/xi1); disp([count xi1,xi, ea]); xi=xil; end Home 1(O noPHP) I Homework 11 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 The root of the function is closest to Choices None 1 5 13 Submit I Attempts 1 1 ILLL
Using the MATLAB code f=inline('x^3 - x^2 -18'); df=inline('3*x^2 - 2*x'); ea=100; count=0; xi=0.5; while (ea>.01); count = count + 13; xil = xi - f(xi)/df(xi); ea = 100*abs(xil-xi)/xi1); disp([count xi1,xi, ea]); xi=xil; end Home 1(O noPHP) I Homework 11 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 The root of the function is closest to Choices None 1 5 13 Submit I Attempts 1 1 ILLL
Computer Networking: A Top-Down Approach (7th Edition)
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Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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![### MATLAB Code for Finding Roots
The following MATLAB code utilizes Newton's method to approximate the root of the function \( f(x) = x^3 - x^2 - 18 \).
```matlab
f=inline('x^3 - x^2 -18');
df=inline('3*x^2 - 2*x');
ea=100;
count=0;
xi=0.5;
while (ea>.01);
count = count + 1;
xi1 = xi - f(xi)/df(xi);
ea = 100*abs((xi1-xi)/xi1);
disp([count xi1,xi, ea]);
xi=xi1;
end
```
### Explanation of Code
- **Function Definition**: The function is defined as \( f(x) = x^3 - x^2 - 18 \) and its derivative \( df(x) = 3x^2 - 2x \).
- **Initial Setup**: The approximate error (`ea`) is initialized to 100, and the initial guess (`xi`) for the root is set to 0.5. The counting variable (`count`) is initialized at 0.
- **Iteration**:
- The loop continues until the approximate error (`ea`) is less than 0.01%.
- Inside the loop, the next approximation of the root (`xi1`) is calculated using the formula \( x_{i+1} = x_i - \frac{f(x_i)}{df(x_i)} \).
- The approximate error is updated and printed along with the iteration count and current approximations.
- The value of `xi` is updated for the next iteration.
### Question
- **Root Approximation**: The root of the function is closest to one of the following choices:
- None
- 1
- 5
- 3
### Interface Elements
- **Choice Selection**: There is a table with selectable options for the root approximation.
- **Homework Navigation**: The interface contains navigation elements for different homework questions, with Q2 highlighted in a different color, indicating the current question.
Submit attempts are limited to 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97234a29-7009-4d8e-8d71-9606bd71717d%2F9faf2454-91c0-439c-814c-0369d357f2fb%2Ftbf9frk_processed.png&w=3840&q=75)
Transcribed Image Text:### MATLAB Code for Finding Roots
The following MATLAB code utilizes Newton's method to approximate the root of the function \( f(x) = x^3 - x^2 - 18 \).
```matlab
f=inline('x^3 - x^2 -18');
df=inline('3*x^2 - 2*x');
ea=100;
count=0;
xi=0.5;
while (ea>.01);
count = count + 1;
xi1 = xi - f(xi)/df(xi);
ea = 100*abs((xi1-xi)/xi1);
disp([count xi1,xi, ea]);
xi=xi1;
end
```
### Explanation of Code
- **Function Definition**: The function is defined as \( f(x) = x^3 - x^2 - 18 \) and its derivative \( df(x) = 3x^2 - 2x \).
- **Initial Setup**: The approximate error (`ea`) is initialized to 100, and the initial guess (`xi`) for the root is set to 0.5. The counting variable (`count`) is initialized at 0.
- **Iteration**:
- The loop continues until the approximate error (`ea`) is less than 0.01%.
- Inside the loop, the next approximation of the root (`xi1`) is calculated using the formula \( x_{i+1} = x_i - \frac{f(x_i)}{df(x_i)} \).
- The approximate error is updated and printed along with the iteration count and current approximations.
- The value of `xi` is updated for the next iteration.
### Question
- **Root Approximation**: The root of the function is closest to one of the following choices:
- None
- 1
- 5
- 3
### Interface Elements
- **Choice Selection**: There is a table with selectable options for the root approximation.
- **Homework Navigation**: The interface contains navigation elements for different homework questions, with Q2 highlighted in a different color, indicating the current question.
Submit attempts are limited to 1.
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