(define dx 0.00001) (define (smooth f) (lambda (x) (/ (+ (f (- x dx)) (f x) (f (+ x dx))) 3))) (define (n-fold-smooth f n) ((repeated smooth n) f))

The above answer for n-fold-smooth is incorrect. The function "repeated" is not used correctly in the function. Repeated should be defined as:

```
(define (repeated f n)
(lambda (x) (cond ((= n 0) x)
(else
((compose (repeated f (- n 1)) f) x)))))
```

And n-fold-smooth (named "n-smooth" below) should be defined as:

```
(define (n-smooth f n x)
((repeated (smooth f) n) x))
```

The first solution is correct

```
(define (n-fold-smooth f n)
((repeated smooth n) f))
```

and the second is incorrect.

```
(define (n-smooth f n x)
((repeated (smooth f) n) x))
```

The input needs only the function and the number of smoothing procedure, so it should not include x. Also in the second solution, we get the n-times composition of (smooth f), instead of the desired n-times composition of (smooth) as a procedure, which is then applied to f.

<< Previous exercise (1.43) | Next exercise (1.45) >>