Solutions to the following problems should consist of program codes, computed results, and short write-ups. In the write-up, discuss the results you have obtained and explain them from the numerical point of view. Use SINGLE PRECISION ONLY. Insert COMMENTS in your programs. Implement Newton's iteration and test it for a nonlinear equations (of your choice) for which you know the root. Make sure that your algorithm does not perform more than 20 iterations, and print both the true error |e_n| = |r - x_n| and its empirical estimate As always provide a short description of the equations and a short discussion of obtained results (e.g., are the empirical error estimates close to the true errors?), with the source-code, and printed computer results