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Exercise 1.44

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Correl Roush 2014-06-02 12:07:43 -04:00
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@ -659,7 +659,23 @@ layout: org
function". Show how to generate the n-fold smoothed function of
any given function using `smooth' and `repeated' from *Note
Exercise 1-43::.
----------------------------------------------------------------------
#+begin_src scheme :tangle yes
;; -------------------------------------------------------------------
;; Exercise 1.44
;; -------------------------------------------------------------------
(define (smooth f)
(lambda (x) (/ (+ (f (- x dx))
(f x)
(f (+ x dx)))
3)))
(define (smooth-n f times)
((repeated smooth times) f))
#+end_src
** Exercise 1.45
We saw in section *Note 1-3-3:: that attempting to compute square
roots by naively finding a fixed point of y |-> x/y does not