2-10.rkt

#lang racket

(define (make-interval a b) (cons a b))

(define (lower-bound interval) (car interval))

(define (upper-bound interval) (cdr interval))


(define (mul-interval x y)
  (let ([p1 (* (lower-bound x) (lower-bound y))]
        [p2 (* (lower-bound x) (upper-bound y))]
        [p3 (* (upper-bound x) (lower-bound y))]
        [p4 (* (upper-bound x) (upper-bound y))])
    (make-interval (min p1 p2 p3 p4)
                   (max p1 p2 p3 p4))))

(define (spans-zero-interval? int)
  (and (>= (upper-bound int) 0)
       (<= (lower-bound int) 0)))

(define (div-interval x y)
  (if (spans-zero-interval? y)
      (error "Can't divide by interval that spans zero")
      (mul-interval x
                    (make-interval (/ 1.0 (upper-bound y))
                                   (/ 1.0 (lower-bound y))))))

(div-interval (make-interval 1 3) (make-interval 1 2))
(div-interval (make-interval 1 3) (make-interval -2 2))