4. Newton's method [20 pts] Use Newton's method to approximate the solution for the function f(x)=2 cos(2x) sin(2x) 2e**. Starting with Xo = 2. Find x and its absolute and relative error in each iteration. 5. Bisection Method [5 pts] Show that the 2x' 6x+1= 0 has a real root in the interval (0,21 using bisection method. (Hint: Intermediate Value Theorem] [10 pts] Use bisection program to approximate another solution in the interval [1,2]. Find your second iteration approximate root value. 6. Gauss-Seidel Method (20 pts] Use Gauss-Seidel Method to approximate the following system of linear equations. Assume the starting guess solution is x = 1, y = 2, z = 3. 4x = 2y - z - 1 X + z = -4 3x - 5y + z = 3