Use Neville's method to obtain the approximations for Lagrange interpolating polynomials of degrees one, two, and three to approximate each of the following:
a. f (8.4) if f (8.1) = 16.94410, f (8.3) = 17.56492, f (8.6) = 18.50515, f (8.7) = 18.82091
b. f(−1/3) if f (−0.75) = −0.07181250, f (−0.5) = −0.02475000, f (−0.25) = 0.33493750, f (0) = 1.10100000
c. f (0.25) if f (0.1) = 0.62049958, f (0.2) = −0.28398668, f (0.3) = 0.00660095, f (0.4) = 0.24842440
d. f (0.9) if f (0.6) = −0.17694460, f (0.7) = 0.01375227, f (0.8) = 0.22363362, f (1.0) = 0.65809197