Estimate a real root of the polynomial f(x) = 5x4-2x3-25x2-6x+45 between x=1 and x=2 (using bisection,...

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)

Expert Solution

samet mamat answered 2 years ago

The Polynomial f(x) = X^3 - X^2 - X -1 has one real root a, which...

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}...

use bisection to find the real root x = sin(x) + 1 with the initial guesses...

use bisection to find the real root x = sin(x) + 1 with the initial guesses of x l = 0 and x u = 3. perform the computation until the approximate error falls below 5%

USING BISECTION METHOD, FIND THE ROOT OF 0.5e^x - 5x + 2 = 0 ON THE...

USING BISECTION METHOD, FIND THE ROOT OF 0.5e^x - 5x + 2 = 0 ON THE INTERVAL [ 0 , 1 ] UP TO 3 DECIMAL PLACES. USE NEWTON'S METHOD TO APPROXIMATE THE ROOT OF f(x)=x^2-5 IN THE INTERVAL [ 2 , 3 ] UP TO 4 DECIMAL PLACES.

f(x)=x^3-3x-1=0 x=[0,2] epsilon=5*10^-2 1. perform the bisection method for the root in [0,2] until your root...

f(x)=x^3-3x-1=0 x=[0,2] epsilon=5*10^-2 1. perform the bisection method for the root in [0,2] until your root is closer to the real root within epsilon. Let x_0=1.0, x_1=1.2 2. perform the secant method until your root is closer to the real root within epsilon. 3. do as in 2. with the Newton's method, with x_0=1.1

Estimate the area A between the graph of the function f(x)= square root of x and...

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

Use the bisection method to approximate the root of f(x)=x-cosx in the range [0.0,1.5]. Stop when...

Use the bisection method to approximate the root of f(x)=x-cosx in the range [0.0,1.5]. Stop when the error is less than 0.002%

(a) For f(x) = 1 4 x 4 − 6x 2 find the intervals where f(x)...

(a) For f(x) = 1 4 x 4 − 6x 2 find the intervals where f(x) is concave up, and the intervals where f(x) is concave down, and the inflection points of f(x) by the following steps: i. Compute f 0 (x) and f 00(x). ii. Show that f 00(x) is equal to 0 only at x = −2 and x = 2. iii. Observe that f 00(x) is a continuous since it is a polynomial. Conclude that f 00(x)...

Using the function f(x)=7x4+2x3+4x2−6x+5 and Descartes' Rule of Signs, what are possible combinations of positive, negative,...

Using the function f(x)=7x4+2x3+4x2−6x+5 and Descartes' Rule of Signs, what are possible combinations of positive, negative, and imaginary zeros? Select all that apply: 2 positive, 2 negative, 0 imaginary 4 positive, 0 negative, 0 imaginary 0 positive, 4 negative, 0 imaginary 0 positive, 2 negative, 2 imaginary 0 positive, 0 negative, 4 imaginary

prove that f(x)=x^2019 +x-1 has only one real root

f(x) = ((x − 1)^2) e^x How easy would it be to apply the Bisection Method...

f(x) = ((x − 1)^2) e^x How easy would it be to apply the Bisection Method compared to Newton's method and modified Newton's method to the function f(x)? Explain.

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