Modify fixed-point so that it prints the sequence of approximations it generates, using the newline and display primitives shown in exercise 1.22 . Then find a solution to x^x = 1000 by finding a fixed point of x → log(1000)/log(x). (Use Scheme's primitive log procedure, which computes natural logarithms.) Compare the number of steps this takes with and without average damping. (Note that you cannot start fixed-point with a guess of 1, as this would cause division by log(1) = 0.)
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(check-equal? (round (* 100 (fixed-point cos 1.0))) 74) (check-equal? (round (* 100 (fixed-point (lambda (y) (+ (sin y) (cos y))) 1.0))) 126)