Problem 2) Compute the backward difference approximation of O(ha) for the first derivative of y = sin x at x = 7/4 using a value of h = 7/12 and determine the true percent relative error et. Take the exact value of the derivative at #/4 to be cos (1) (1) = 0.70710678. The values of f(x) at the points Xi, Xit1 = x; h, Xi+2 = Xi 2h, are given below. You may not need all of the information in the table. Keep two decimal-place accuracy. Xi-2 Xi-1 f(x) 0.261799388 0.258819045 0.523598776 0.5 0.785398163 0.707106781 1.047197551 0.866025404 1.308996939 0.965925826 Xi Xi+1 Xi+2 Show steps! Problem 3) Compute the centered difference approximation of O(h4) for the first derivative of y = sin x at x = 7/4 using a value of h = 7/12 and determine the true percent relative error t. Take the exact value of the derivative at 7/4 to be cos 0.70710678. The values of f(x) at the points Xi, Xi+1 = XiEh, Xi+2 = Xi + 2h, are given below. You may not need all of the information in the table. Keep two decimal-place accuracy. TT X 1-2 X1-1 f(x) 0.261799388 0.258819045 0.523598776 0.5 0.785398163 0.707106781 1.047197551 0.866025404 1.308996939 | 0.965925826 X i Xi+1 Xi+2 Show steps! Problem 2) Compute the backward difference approximation of O(ha) for the first derivative of y = sin x at x = 7/4 using a value of h = 7/12 and determine the true percent relative error et. Take the exact value of the derivative at #/4 to be cos (1) (1) = 0.70710678. The values of f(x) at the points Xi, Xit1 = x; h, Xi+2 = Xi 2h, are given below. You may not need all of the information in the table. Keep two decimal-place accuracy. Xi-2 Xi-1 f(x) 0.261799388 0.258819045 0.523598776 0.5 0.785398163 0.707106781 1.047197551 0.866025404 1.308996939 0.965925826 Xi Xi+1 Xi+2 Show steps! Problem 3) Compute the centered difference approximation of O(h4) for the first derivative of y = sin x at x = 7/4 using a value of h = 7/12 and determine the true percent relative error t. Take the exact value of the derivative at 7/4 to be cos 0.70710678. The values of f(x) at the points Xi, Xi+1 = XiEh, Xi+2 = Xi + 2h, are given below. You may not need all of the information in the table. Keep two decimal-place accuracy. TT X 1-2 X1-1 f(x) 0.261799388 0.258819045 0.523598776 0.5 0.785398163 0.707106781 1.047197551 0.866025404 1.308996939 | 0.965925826 X i Xi+1 Xi+2 Show steps