lIZI'onsider the function f{} = s5 2:3 3:2 + :r: l. {a} Find the Lagrange interpolating polynolniah ngmjr of degree at most 2 for f {:12} using In = 1m1= 15132; =1. ' ' {b} live the general error formula [or at} Pzifi}. to} Use the formula from {h} to nd a hound for the absolute error at :r: = {Li}. Be sure to give your reasoning. {d} lC'ompare your error hound to actual error at a: = I'll}. Is the error hound reasonable? {e} Now1 suppose In = and 3:1 = h, 323 = 211 for some h, :3 fl. How small must la. over the internal [F], 2h] he chosen so that the absolute error is guaranteed to he less than iii\"'1