Using Fixed-Point Iteration with x, (cos x, +1), wha tenth iteration? Use x, 0.50. A. 0.06258608 B. 0.60710165 C. 0.60712645 D. 0.60710254
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- find the root value of the f(x) function at the end of the 2nd iteration under the initial condition x0=1. Use the Newton-Raphson method. Take the stopping tolerance 1e-5.For every question below:• Use appropriate initial guesses• Calculate the relative approximate error after every iteration• Conduct 3 iterations• Indicate how many significant figures you can trust in your approximation and why? Bisection Method: 1. Use the bisection method to approximate the root of f(x)= ln (x) + x2 2. Use the bisection method to approximate x in x3= 123. Use the bisection method to approximate where the graphs y= x3 and y= x + 1Using NEWTON’S METHOD, determine new estimate after 2nd iteration.\ ε = 0.001 x0 = 1.500
- make a table to compare the indicated values of y(x) by Euler's method, the improved Euler method and the RK4 method. Calculate by rounding to four decimal places. First use h 0.1 years after h 0.05.Find the root of the equation f(x) = ex − 3 using the methods in (a), (b), and (c). For all methods, use a percent relative approximate error tolerance of 10%. Carry out your iterations using 5 decimal digitsCalculate the root of the function f (x) = e ^ x cos x between -5 and +3 by the Newton-Raphshon method. In the table you have created, take your first guess (where n = 0) '1 and make the margin of error 10 ^ -6'.x0 = 0.1x1 = 1st guessx2 = 2nd guessx3 = 3rd guessx4 = 4th guessx5 = 5th guessIf you sort your predictions in the iteration, what is the 2nd predictor value to x2?
- Find an approximate solution of the first root of the following function using the secant method. Consider the interval [0,1-0,5] with an allowable error of 10^-2Implement the Gauss-Jacobi Method. Iterate until the Relative True Error is less than 0.00001. Start at x=1 for all values of x. Determine: 1. What is the value of x6 at the 6th iteration? 2. What is the value of x7 at the 5th iteration? 3. What is the value of x3 at the 11th iteration? 4. What is the value of x4 at the 9th iteration?Using GAUSS-JACOBI iteration, what is y after the 5th iteration? [use 5 decimal places] a. Using GAUSS-SIEDEL iteration, what is x?
- Considering the equation f(x) = x – cos(x), the value of εa of the third iteration using Regula-Falsi method is? Use [0,1] as your initial guess.Group of answer choices 0.078% 0.001% 0.018% 0.358%Integrate the following functions analytically and numerically. Use the Trapezoidal method to numerically integrate with n=4. Calculate the error against the analytical results.This time implement the iteration process using Newton-Raphson and Secant Method. Use the initial values of 0 or 1 or both when applicable. The pre specified error accepted is 0.0001.