Use Newtons method to find a solution accurate to within 10-2 for ex-3x2=0, 0≤ x≤ 1 (Numerical Methods/Analysis)
Use Newtons method to find a solution accurate to within 10-2 for ex-3x2=0, 0≤ x≤ 1...
3. Use Newton's method to find solution accurate to within 10-3 for x3 + 3x2 – 1 = 0 on (-3,-2]. Use po -2,5. 4. Use Secant method to find the solution P4 for In(x - 1) + cos(x - 1) = 0 on [1.3,2]. Use po 1.3 and p1 = 1.5. 5. Use False position method to find the solution P4 for 3x – e* = 0 on [1,2]. Use - Ро 1 and P1 2.
(1) Use the Bisection method to find solutions accurate to within 10-2 for x3 – 7x2 + 14x – 6 = 0 on the interval [3.2, 4]. Using 4-digit rounding arithmatic. (2) Consider the function f(x) = cos X – X. (a). Approximate a root of f(x) using Fixed- point method accurate to within 10-2 . (b). Approximate a root of f(x) using Newton's method accurate to within 10-2. Find the second Taylor polynomial P2(x) for the function f(x) =...
Question 2 (20 Points) (1) Use the Bisection method to find solutions accurate to within 10-2 for x3 - 7x2 + 14x - 6 = 0 on the interval [3.2, 4]. Using 4-digit rounding arithmatic. (2) Consider the function f(x) = cos x - x. (a). Approximate a root of f(x) using Fixed-point method accurate to within 10-2 (b). Approximate a root of f(x) using Newton's method accurate to within 10-2.
MATLAB Newtons Method. Use initial guess of xo. Use Matlab. x2-3x2+ 3x - 1 = 0
2. [10 pts ] Use fixed-point iteration to determine a solution accurate to within 10-3 for f(x) x - cos(x)/2, for x in [ 0,1]. Use your calculator to calculate values, but be sure to show what values are being calculated. (a) show the function g(o) that you use: (b) show the initial value po that you use: (c) show the computations for the successive values of the pi until convergence: 2. [10 pts ] Use fixed-point iteration to determine...
Golden ratio method is recommended by the solution and the numerical solution is 4.493335656115932 (or anything accurate up to 2 dp) (2) Maximum of a function We consider the function, f(x) = ( Sinar Provided that there is a local maximum in the interval r 4,5. Please find this local maximum with accuracy up to two decimal places. You need to prove that the desired accuracy is reached so that you can stop. You can use any methods you know....
Find solution using Simplex method (BigM method) MAX Z = 5x1 + 3x2 + 2x3 + 4x4 subject to 5x1 + x2 + x3 + 8x4 = 10 2x1 + 4x2 + 3x3 + 2x4 = 10 X j > 0, j=1,2,3,4 a) make the necessary row reductions to have the tableau ready for iteration 0. On this tableau identify the corresponding initial (artificial) basic feasible solution. b) Following the result obtained in (a) solve by the Simplex method, using...
10. Use the Method of Variation of Parameters to find a particular solution for the differential equation y" +y= ex (You may use the integral formulas Íe' sin xax= ex (sin x-cos x) + c and「' cos xdr= e"(sin x + cos x) + c. )
both please 1. Use the method of separation of variables find the general (explicit) solution to the differential equation = xcscy dy 2. Find the general solution to the first-order linear differential equation dy ex x + 2y = dx X by finding an appropriate integrating factor. (No credit for any other method). Give an explicit solution. 0
chose on of the two ? Find a Frobenius series solution for x > 0. Use the small index. 4x2 y" + 9xy' + (-3x2 + 1) y = 0) 4x2 y" + 7xy' - (2x2 + 1) y= 0) or