The Polynomial f(x) = X^3 - X^2 - X -1 has one real root a,
which happens to be positive. This real number a satisfies the
following properties:
- for i = 1,2,3,4,5,6,7,8,9,10, one has {a^i} not equal to
zero
- one has
[a] = 1, [a^2] = 3, [a^3] = 6, [a^4] = 11, [a^5] = 21, [a^6] =
7, [a^7] = 71, [a^8] = 130
(for a real number x, [x] denotes the floor of x and {x}...
Determine the root of
f (x) = 10.5X² - 1.5X - 5
by using Newton Raphson method with x0 = 0 and perform the
iterations until ɛa < 1.00%.
Compute ɛt for each approximation if given the true root is x =
0.7652.
Estimate a real root of the polynomial
f(x) = 5x4-2x3-25x2-6x+45 between
x=1 and x=2 (using bisection, Standard Newton-Raphson, Secant, and
modified Newton-Raphson, and modified Secant methods). Show the
detailed calculations for 5 iterations (for each method)
Determine the positive real root of ln(x^2)=0.8 by the following
methods. (Note that you need to show the details of your
derivations in MATLAB).
a) Graphically ( plot the function and copy your figure to
word).
b) Using two iterations of the bisection method with initial
guesses of xl=0.4 and xu=2 and populate the following table. What
is the root after two iterations? Provide justification for the
values you have obtained in your MATLAB code as comments.
i xl xu...
Consider the function f(x) = x - xcosx, which has a root at x =
0. Write a program to compare the rates of convergence of the
bisection method (starting with a = -1, b = 1) and Newton’s method
(starting with x = 1). Which method converges faster? Why?
Write a Matlab function for:
1. Root Finding: Calculate the root of the equation f(x)=x^3
−5x^2 +3x−7
Calculate the accuracy of the solution to 1 × 10−10. Find the
number of iterations required to achieve this accuracy. Compute the
root of the equation with the bisection method.
Your program should output the following lines:
• Bisection Method: Method converged to root X after Y
iterations with a relative error of Z.
Estimate the area A between the graph of the function f(x)=
square root of x and the interval [0,49]. Use an approximation
scheme with n=2,5, and 10 rectangles. Use the right
endpoints.
Round your answers to three decimal places.
A2=
A5=
A10=
Click