1.7

 
(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)) 0.001))
​
(define (square x) (* x x))
​
(sqrt-iter 1 0.0001)
​x
 
0.03230844833048122

 
(sqrt 0.0001)
 
0.01

$\Delta$ =

 
(- 0.03230844833048122 (sqrt 0.0001))
 
0.02230844833048122

$\Delta\%$ =

 
(/ (- 0.03230844833048122 (sqrt 0.0001)) 0.0001)
 
223.08448330481218

Design and Implementation of better sqrt-iter:

 
(define (sqrt-iter lastGuess guess x)
  (if (good-enough? lastGuess guess)
      guess
      (sqrt-iter guess (improve guess x) x)
      )
  )
​
(define (good-enough? lastGuess guess)
  (< (abs (- lastGuess guess)) 0.001)
  )
 
#<undef>

Compare to the previous example:

 
(sqrt-iter 1 100 0.0001)
 
0.010028540197249

 
(sqrt 0.0001)
 
0.01

$\Delta$ =

 
(- 0.010028540197249 (sqrt 0.0001))
 
0.00002854019724900063

$\Delta\%$ =

 
(/ (- 0.010028540197249 (sqrt 0.0001)) 0.0001)
 
0.28540197249000626