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Exercise_2_9.rkt
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Exercise_2_9.rkt
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#lang racket/base
(define (make-interval a b) (cons a b))
(define (upper-bound interval)
(max (car interval) (cdr interval)))
(define (lower-bound interval)
(min (car interval) (cdr interval)))
(define (add-interval x y)
(make-interval (+ (lower-bound x) (lower-bound y))
(+ (upper-bound x) (upper-bound y))))
(define (sub-interval a b)
(add-interval
a
(make-interval
(- (lower-bound b))
(- (upper-bound b)))))
(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 (div-interval x y)
(mul-interval
x
(make-interval (/ 1.0 (upper-bound y))
(/ 1.0 (lower-bound y)))))
(define (interval-width interval)
(/ (- (upper-bound interval) (lower-bound interval)) 2))
(define a (make-interval 3 4))
(interval-width a)
; 1 / 2
(define b (make-interval 1 2))
(interval-width b)
; 1 / 2
(add-interval a b)
; '(4 . 6)
(interval-width (add-interval a b))
; 1
(sub-interval a b)
; '(1 . 3)
(interval-width (sub-interval a b))
; 1
(mul-interval a b)
; '(3 . 8)
(interval-width (mul-interval a b))
; 2 1/2
(div-interval a b)
; '(1.5 . 4.0)
(interval-width (div-interval a b))
; 1.25