sicp习题解答1.3.2 - 1.3.3

上一节1.3.1

;;Exercise 1.34
(define (f g)
  (g 2))

;;Exercise 1.35
(define tolerance 0.00001)
(define (fixed-point f first-guess)
  (define (close-enough? v1 v2)
    (< (abs (- v1 v2)) tolerance))
  (define (try guess)
    (let ((next (f guess)))
      (if (close-enough? guess next)
          next
          (try next))))
  (try first-guess))

(fixed-point (lambda (x) (+ 1 (/ 1 x))) 1.0)



;;Exercise 1.36
(define (fixed-point f first-guess)
  (define (close-enough? v1 v2)
    (< (abs (- v1 v2)) tolerance))
  (define (try guess)
    (display guess)
    (newline)
    (let ((next (f guess)))
      (if (close-enough? guess next)
          next
          (try next))))
  (try first-guess))

(define (average x y)
  (/ (+ x y) 2))


;take with average damping
(fixed-point (lambda (x)(average x (/ (log 1000) (log x)))) 5)
;without average damping
(fixed-point (lambda (x) (/ (log 1000) (log x))) 5)


Welcome to DrScheme, version 372 [3m].
Language: Standard (R5RS).
5
4.64601483711009
4.571611286076025
4.558294317536066
4.556006022881116
4.555615799731297
4.555549342575593
4.555538027101999
4.5555361005218895


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4.29202967422018
4.741863119908242
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4.635299887107611
4.50397811613643
4.589989462723705
4.53301150767844
4.570475672855484
4.545720389670642
4.562024936588171
4.551263234080531
4.55835638768598
4.553676852183342
4.55676216434628
4.554727130670954
4.556069054770006
4.555184018843625
4.5557676565438205
4.555382746639082
4.55563658243586
4.555469180245326
4.555579577900997
4.5555067722873686
4.5555547860484085
4.555523121789556
4.555544003742869
4.555530232469306
4.555539314360711
>

;;Exercise 1.37
(define (cont-frac n d k)
  (define (iter i)
    (if (= i k)
        (/ (n k) (d k))
        (/ (n i) (+ (d i)
                    (iteer (+ i 1))))))
  (iter 1))

(cont-frac (lambda (i) 1.0)
           (lambda (i) 1.0)
           12)



;;Exercise 1.38
(define (e-2)
  (define (d i)
    (if (= (remainder i 3) 2)
        (* (/ (+ i 1) 3) 2)
        1))
  (cont-frac (lambda (i) 1.0)
             d
             12))
(e-2)



;;Exercise 1.39
(define (tan-cf x k)
  (cont-frac (lambda (i) (if (= i 1) x (- (square x))))
             (lambda (i) (- (* 2 i) 1))
             k))