math based. i need help in 20.

19. Explore the idea of Example 1.6 for cube roots. If x is a guess that is smaller than A3 then A/a2 will be larger than A1/3, so that the average of the two will be a better approximation than x. Suggest a Fixed-Point Iteration on the basis of this fact, and use Theorem 1.6 to decide whether it will converge to the cube root of A. 20. Improve the cube root algorithm of Exercise 19 by reweighting the average. Setting g) wx -w)A/ for some fixed number 0w