[15 marks] Problem 1: Find a root nearx = 2 of x = 2sin(x) using Newton Raphsons method Do 3 iterations. [15 marks] Problem 2: Solve the illowing system of equations using the GaussSeidel method. Rearrange the equations if needed for convergence. Do 3 iterations only. Choose: [X1 X2 X3] = [0.9 1.2 2.5] as the initial guess. NOTE: no need to calculate the error at each iteration. 3X1" Xg X3=2 X1\"2X2+4X3=17 2X16X2+ X3=-? [25 marks] Problem 3: Fit the following data with the power model (y = g). Usethe resulngpowerequationtopredictyatx= 9. _1' 13 11 8.5 3.1 '3' 6.2 5.3 4.8 4.6 4.3 Note #1: Students are allowed to linearize data. Note #2: log/g?) = h*log{x). [2]} marks] Problem 4: Use 2point Gauss Quadrature formula to calculate: 1'3\" log (1 + 1') d1. [25 marks] Problem 5: Estimate 32(1) by solving the following Tilorder ODE using Heun's method. Assume F2 = 0.5 seconds. dam?\" + me: = surly), my) =1. and game) = 2