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Feb 24th, 2018
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  1. if
  2.  
  3. (define (sqroot x)
  4. (sqrt-iter 1.0 x))
  5. (define (sqrt-iter guess x)
  6. (if (good-enough? guess x)
  7. guess
  8. (sqrt-iter (improve guess x)
  9. x)))
  10. (define (good-enough? guess x)
  11. (< (abs (- (square guess) x)) 0.001))
  12. (define (improve guess x)
  13. (average guess (/ x guess)))
  14. (define (average x y)
  15. (/ (+ x y) 2))
  16. (define (square x)
  17. (* x x))
  18.  
  19. Example:
  20. 1) (sqroot 4)
  21. 2) (sqrt-iter 1 4)
  22. 3) (if (good-enough? 1 4)
  23. 1
  24. (sqrt-iter (improve 1 4)
  25. 4))
  26. 4) (good-enough? 1 4)
  27. (< (abs (- (square 1) 4)) 0.001))
  28.  
  29. 5) (square 1)
  30. (* 1 1)
  31.  
  32. Answer: 1
  33.  
  34. 6) (< (abs (- 1 4)) 0.001))
  35. (< (abs -3) 0.001))
  36. (< 3 0.001))
  37.  
  38. Answer: #false
  39.  
  40. 7) (sqrt-iter (improve 1 4)
  41. 4)
  42.  
  43. 8) (average 1 (/ 4 1)))
  44.  
  45. 9) (/ 4 1)
  46.  
  47. Answer: 4
  48.  
  49. 10) (average 1 4))
  50. 11) (/ (+ 1 4)
  51. 2))
  52. 12) (+ 1 4)
  53.  
  54. Answer: 5
  55.  
  56. 13) (/ 5 2)
  57.  
  58. Answer: 2.5
  59.  
  60. 14) (sqrt-iter 2.5 4)
  61. 15) p.3 etc.
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