By treating Newton's method as considered in part (b) as an iterative map, Pn+1 = g(Pn), show that the absolute error, En = |p - Pn|, satisfies lim n->[infinity] En+1 / En^2 = 2^-2/3, and deduce the order of convergence of the iteration. Hint: write a Taylor series for g in powers of (Pn - p).