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sicp exercise 1.8

; 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.) (begin (define ( cube-root x ) (define (good-enough? guess p) ( < (abs (- p ( * guess guess guess) )) 0.000001) ) (define (improve guess x) (/ ( + (/ x (* guess guess)) (* 2 guess)) 3) ) (define (cube-root-impl x guess) ( if (good-enough? guess x) guess (cube-root-impl x (improve guess x)) ) ) (cube-root-impl x 1.0 ) )(display (cube-root 125)) (newline))

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