Ex-2.13-todo

-

Ex-2.12

(define (make-center-percent c p)
  (let ((width (/ (* c p) 100)))
    (make-center-width c width)))
(define (percent i)
  (let ((w (width i))
        (c (center i)))
    (/ (* w 100) c))) 

Ex-2.11 - todo

todo

Ex-2.10

(define (div-interval x y)
  (if (or (= (lower-bound y) 0)
          (= (upper-bound y) 0))
      (error ("division by zero"))
      (mul-interval
       x
       (make-interval
        (/ 1.0 (upper-bound y))
        (/ 1.0 (lower-bound y)))))) 

Ex-2.9

Using the add-interval definition, for add-interval:

width(x+y) =  (upper-bound(x) + upper-bound(y))
            - (lower-bound(x) + lower-bound(y))
           = width(x) + width(y) 

Using the sub-interval definition, for sub-interval

width(x-y) = (upper-bound(x) - lower-bound(y))
           -(lower-bound(x) - upper-bound(y))
          = width(x) + width(y) 

Ex-2.8

(define (sub-interval x y)
  (make-interval
   (- (lower-bound x) (upper-bound y))
   (- (upper-bound x) (lower-bound y)))) 

Ex-2.7

(define (make-interval a b)
  (cons (min a b) (max a b)))
(define (lower-bound interval)
  (car interval))
(define (upper-bound interval)
  (cdr interval))