SICP练习1.6-1.8

1.6　　

死循环

1.7

 #lang racket
 (define (square x) (* x x))
 (define (sqrt-iter guess x)
   (if (good-enough? guess x)
       guess
       (sqrt-iter (improve guess x)
                  x)))
 (define (improve guess x)
   (average guess (/ x guess)))

 (define (average x y)
   (/ (+ x y) ))

 (define (good-enough? guess x)
   (< (abs (- (/ (square guess) x) ) ) .))

 (define (sqrt x)
   (sqrt-iter . x))

 (sqrt .)

1.8立方根的牛顿法

 #lang racket
 (define (power3 x) (* x x x))
 (define (square x) (* x x))
 (define (curo-iter guess x)
   (if (good-enough? guess x)
       guess
       (curo-iter (improve guess x)
                  x)))
 (define (improve guess x)
   (average3 (*  guess) (/ x (square guess))))
 (define (average3 x y)
   (/ (+ x y) ))
 (define (good-enough? guess x)
   (< (abs (- (/ (power3 guess) x) ) ) .))
 (define (curo x)
   (curo-iter . x))

 (curo )