Lista 1 z MP

#lang racket

;; ćw. 4

(define (square x) (* x x))

(define (sum-of-squares x y) (+ (square x) (+ (square y))))

(define (sum-of-greater x y z)
  (cond [(and (> x z) (> y z)) (sum-of-squares x y)]
        [(and (> x y) (> z y)) (sum-of-squares x z)]
        [else (sum-of-squares y z)]))

;; ćw. 6

(define ex-for-and
  (and (< 10 3) (= 2 (/ 4 0))))

(define ex-for-or
  (or (= 2 2) (= 0 (/ 12 0))))

;; ćw. 7

(define (power-close-to b n)
  (define (wykladnik e)
    (if (> (expt b e) n)
        e
        (wykladnik (+ e 1))))
  (wykladnik 0))


;; pracownia

(define (cube x) (* x x x))

 (define (aux x y)
   (/ (+ x (* 2 (cube y))) (* 3 (square y))))

(define (dist x y)
  (abs (- x y)))

(define (cube-root x)
  (define (improve approx)
    (aux x approx))
  (define (good-enough? approx)
    (< (dist x (cube approx)) 0.0001))
  (define (iter approx)
    (if (good-enough? approx)
        approx
        (iter (improve approx))))

  (iter 1.0))