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Exercise 1.8

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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/(y^2) + 2y)/3.

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.)

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