Numerical Analysis . Question 2. Using python

e tR Wilkinson polynomial. (a) Prove that W'(16) 1514! (b) Find an analogous formula for W,(j) , where j s an integer between 1 and 20. Let /(x) = x"-ax"-1, and set g(x) = x". (a) Use the Sensitivity Formula to give a prediction for the nonzero root offe (x) = x"-ax"-1 + x" for small (b) Find the nonzero root and compare with the prediction. 8. omputer Problems 1. Let f(x)sin x. (a) Find the multiplicity of the rootr 0. (b) Use MATLAB's lutions for ter Problems d in blue can at VKST9B fzero command with initial guess x -0.1 to locate a root. What are the forward and backward errors of fzero's response? 2. Carry out Computer Problem 1 for f(x) sinx3-x3 3. (a) Use f zero to find the root off(x) = 2x cos x-2x + snx3 on(-0.1, 0.21. Report the forward and backward errors. (b) Run the Bisection Method with initial interval I-0.1,0.2] to find as many correct digits as possible, and report your conclusion. 4. (a) Use (1.21) to approximate the root near 3 of fe (x)-(1 +e)r3-3x2-3 for a constant e. (b) Setting e 103 find the actual root and compare with part (a). 11%, Page 53 of 672