HWS questions - Numerical Method Spring 2022, Due April 10th Calculate your factorf as the very first thing in answering hw questions. f=max(0.15, (31/100). Q1. Use following dataset to calculate the value of f(3.4) using (a) Newton's polynomial method of order 1 through 3 (6) Lagrange's polynomial of order 1 through 3. X1-3+3f X2-4-31 X3-2.5+3f X4-5 f(x1)-7 f(x2)=3 f(x3)-6.5 f(x4)-1 Q2. Evaluate the following integral: [-end (a) analytically, (b) single application of the trapezoidal rule, (c) composite trapezoidal rule with 2 = 2 and 4, (a) single application of Simpson's 1/3 rule, e composite Simpson's 1/3 rule with n = 4 (1) Simpson's 3/8 rule, and (g) com- posite Simpson's rule, with = 5. For each of the numerical estimates (b) through (9) determine the true percent relative error based on (a)