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:

(x/y²+2y)/3

(a) Use this formula to implement a cube-root procedure analogous to the square-root procedure from the lecture notes.

(b) Modify your original implementation to allow the good-enough? procedure to be included as a argument to the cube-root procedure; i.e., (cube-root 3 good-enough?). In this way, roots of arbitrary precision should be possible by defining new forms of good-enough?

 

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