Suppose the following extrapolation table has been constructed to approximate the number M with M = N1(h)

Question:

Suppose the following extrapolation table has been constructed to approximate the number M with M = N1(h) + K1h2 + K2h4 + K3h6:

a. Show that the linear interpolating polynomial P0,1(h) through (h2, N1(h)) and (h2/4, N1(h/2)) satisfies P0,1(0) = N2(h). Similarly, show that P1,2(0) = N2(h/2).
b. Show that the linear interpolating polynomial P0,2(h) through (h4, N2(h)) and (h4/16, N2(h/2)) satisfies P0,2(0) = N3(h).