Programming Question

please solve it without taken form internet i don’t wnat a 0

MATLAB Programming Assignment
Rules:
1. This assignment should be solved using Matlab (or Octave Online).
2. The work you submit should be your own effort (else you may get zero).
3. Do not share your work/solutions with other students.
4. Your submission should include the code, a brief discussion of the code/logic,
graphs and screenshots with results, and a brief analysis/discussion of the
results.
Due: Dec. 17, 2023
1. Consider the following polynomial: f(x) = 4×3 + 6×2 – 27x – 15
Write a program to estimate all the roots of f(x) graphically. The roots are
located between x = -5 and x = 5. [5%]
2. Find the roots of the polynomial in question 1 above using the following
methods and perform iterations until the approx. error becomes less than
0.01%. Also, comment on the accuracy and convergence rate of each method.
a. Bisection method [5%]
b. Simple fixed-point iteration method [5%]
c. Newton-Raphson method [5%]
3. Write a program to estimate the root of f(c) using the false-position method and
generate a table similar to the one shown below. Repeat iterations until the
approximate error becomes less than 0.5%. [10%]
4. Repeat exercise 3 using the Secant method. Repeat iterations until the
approximate error becomes less than 0.1%. [10%]
a. Which method is better? Secant or False-position?
5. Write a program to find the integral of f(x) using multiple application of the
Trapezoidal rule and generate the table and graph shown below: [20%]
The table above shows the integral of f(x) for different intervals based on n
where n is raised to a power of 2. For example, if the user enters n = 4, your
program should generate values for all intervals 20, 21, 22, 23, and 24 ( = 1, 2, 4,
8, and 16).
6. Write a program to find the integral of f(x) using multiple application of the
Simpson’s 1/3 rule and generate the table and graph shown below: [20%]
The table above shows the integral of f(x) for different intervals based on n
where n is raised to a power of 4. For example, if the user enters n = 3, your
program should generate values for all intervals 40, 41, 42, and 43 ( = 1, 4, 16,
and 64).
7. Write a program to find the maximum of the given function using the goldensection search method and generate a table similar to the one shown below.
[20%]
f(x) = 2sinx – x2/10