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) 2))

(define (good-enough? guess x)
  (< (abs (- (/ (square guess) x) 1) ) 0.00001))

(define (sqrt x)
  (sqrt-iter 1.0 x))


(sqrt 0.002)

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 (* 2 guess) (/ x (square guess))))
(define (average3 x y)
  (/ (+ x y) 3))
(define (good-enough? guess x)
  (< (abs (- (/ (power3 guess) x) 1) ) 0.00001))
(define (curo x)
  (curo-iter 1.0 x))

(curo 27)