1.7.txt

Suppose x is a very small number, negligible compared to 0.001.
Given that guess tends to the square root of x wich is negligible
compared to 0.001 too, there will be a time where guess^2 will be
less than 0.001.  But then we have
     | guess^2 - x| < 0.001
So the procedure terminates giving a bad approximation of the square
root of x. As an example we have
(sqrt .0000000000000001)
-> 0.03125000000000106
(square 0.03125000000000106)
-> 0.0009765625000000664

Suppose now that x is very large number, so the square root of x
is also a very large number.  Consequently, guess will take very
large values.  But a real computer have a limited precision, so guess
will be approximated with an error e.  But then we have,
(guess+e)^2 - x = (guess^2 - x) + 2e guess + e^2

Given that the term 2e guess is not negligible if guess is a very
large number, and guess^2 - x tends to 0, we will always have
(guess+e)^2 - x > 0.001.  So the process won't terminate.

(define (good-enough? guess x)
  (< (abs (- (/ (improve guess x)
		guess)
	     1))
     0.001))