练习1.35-练习1-38

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版权声明：本文为博主原创文章，转载请注明出处：http://blog.jerkybible.com/2014/01/11/2014-01-11-练习1.35-练习1-38/

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1.练习1.35

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

2.练习1.36不用平均阻尼方式：

(fixed-point-display (lambda (x) (/ (log 1000) (log x))) 2.0)

结果为：

2.
9.965784284662087
3.004472209841214
6.279195757507157
3.759850702401539
5.215843784925895
4.182207192401397
4.8277650983445906
4.387593384662677
4.671250085763899
4.481403616895052
4.6053657460929
4.5230849678718865
4.577114682047341
4.541382480151454
4.564903245230833
4.549372679303342
4.559606491913287
4.552853875788271
4.557305529748263
4.554369064436181
4.556305311532999
4.555028263573554
4.555870396702851
4.555315001192079
4.5556812635433275
4.555439715736846
4.555599009998291
4.555493957531389
4.555563237292884
4.555517548417651
4.555547679306398
4.555527808516254
4.555540912917957
;Value: 4.555532270803653

平均阻尼的方法：

(fixed-point-display (lambda (x) (/ (+ (/ (log 1000) (log x)) x) 2.0)) 2.0)

结果是：

2.
5.9828921423310435
4.922168721308343
4.628224318195455
4.568346513136242
4.5577305909237005
4.555909809045131
4.555599411610624
4.5555465521473675
;Value: 4.555537551999825

3.练习1.37a）

(define (cont-frac n d k)
  (define (cont-prac-recur n d a k)
    (if (= a k)
	(/ (n k) (d k))
	(/ (n a) (+ (d a) (cont-prac-recur n d (+ a 1) k)))))
  (cont-prac-recur n d 1 k))

k为11时得到的近似值具有十进制的4位精度b）
迭代计算过程：

(define (cont-frac n d k)
  (define (cont-prac-iter a result)
    (cond ((= a k) (cont-prac-iter (- a 1) (/ (n k) (d k))))
	  ((= a 0) result)
	  (else (cont-prac-iter (- a 1) (/ (n a) (+ result (d a)))))))
  (cont-prac-iter k 0))

4.练习1.38

(define (dfc-k k)
  (+ (cont-frac (lambda (i) 1.0)
(lambda (i) (if (= (remainder i 3) 2)
(* (+ (floor (/ i 3)) 1) 2)
1))
k
) 2))

5.练习1.39

(define (tan-cf x k)
  (cont-frac (lambda (i) (if (= i 1)
			     x
			     (- 0 (square x))))
	     (lambda (i) (+ (* (- i 1) 2) 1))
	     k
	     ))