Newton's method for cube roots is based on the fact that if
y
is an approximation to the cube root ofx
, then a better approximation is given by the value:
((x/(y**2)) + 2*y) / (3)
Use this formula to implement a cube-root procedure analogous to the square root procedure.
(define (improve guess x)
(/ (+ (/ x (* guess guess) )
(* 2 guess))
3
)
)
(define (cube x)
(* x x x)
)
(define (good-enough? guess x)
(< (abs (- (cube guess) x)) 0.001)
)
(define (cube-root-iter guess x)
(if (good-enough? guess x)
guess
(sqrt-iter (improve guess x) x)
)
)
(define (cube-root x)
(cube-root-iter 1.0 x)
)