Chapter 4.2, Problem 13ES

a.

To determine

To show: The linear interpolating polynomial $P_{0,1}\left(h\right)$ through $\left(h^2,N_1\left(h\right)\right)\text{ and }\left(\frac{h^2}{4},N_1\left(\frac{h}{2}\right)\right)$ satisfies $P_{0,1}\left(0\right)=N_2\left(h\right)$.

b.

To determine

To show: The linear interpolating polynomial $P_{0,2}\left(h\right)$ through $\left(h^4,N_2\left(h\right)\right)\text{ and }\left(\frac{h^4}{16},N_2\left(\frac{h}{2}\right)\right)$ satisfies $P_{0,2}\left(0\right)=N_3\left(h\right)$.