Assignment:
Eq. P_n (x)=f[x_0 ]+∑_(k=1)^n?f[? x_0,x_1,…,x_k](x-x_0)…(x-x_(k-1))
Q1. Use Eq. to construct interpolating polynomials of degrees one, two, and three for the following data. Approximate the specified value using each of the polynomials.
a. f(0.43) if f(0)=1,f(.25)=1.64872 f(.5)=2.71828,f(.75)=4.48169
b. f(0) if f(-.5)=1.93750,f(-.25)=1.33203,f(.25)=.800781,f(.5)=.687500
Provide complete and step by step solution for the question and show calculations and use formulas.