Exercise 1.8. Newton’s method for cube roots is based on the fact that if y is an approximation to the cube root of x, then a better approximation is given by the value
Use this formula to implement a cube-root procedure analogous to the square-root procedure. (In section 1.3.4 we will see how to implement Newton’s method in general as an abstraction of these square-root and cube-root procedures.)
Solution