Renat Bashirov

//==========================PART 1(EXAMPLE 8)========================================
let functionB (x : float) = 1. / (2. * x - 5.)
let eps = 0.001

let rec iter f init a b =
    if a <= b then f a (iter f init (a + 1) b)
    else init
let power x n = iter (fun z acc -> float(acc) * x) 1. 1 n
let functionTaylorSeries (x : float) =
    let realValue =
        functionB x
    let rec iterTillGotRealValue (acc : float) i =
        if (abs (realValue - acc) < eps)
            then (acc,i)
            else iterTillGotRealValue (acc - float(power 2. i) * float(power x i) / float(power 5. (i+1))) (i+1)
    iterTillGotRealValue 0. 0

let functionTaylorSeriesFaster (x : float) =
    let realValue =
        functionB x
    let rec iterTillGotRealValue (acc : float) (acc4Component : float) i =
        //printf "%f\n" acc
        if (abs (realValue - acc) < eps)
            then (acc,i)
            else iterTillGotRealValue (acc - acc4Component) (acc4Component * 2. * x / 5.) (i+1)
    iterTillGotRealValue 0. 0.2 0

printf "x\tПервый способ\tКол-во итераций\tВторой способ\tКол-во итераций\tЗначение функции\n"
let n = 10
for i = 0 to n do
    let point x =
        2. * float(x) / float(n)
    let x =
        point(i)
    let res1 =
        functionTaylorSeries x
    let res2 =
        functionTaylorSeriesFaster x
    printf "%f\t%f\t%d\t%f\t%d\t%f\n" x (fst res1) (snd res1) (fst res2) (snd res2) (functionB x)


//==========================PART 2(EXAMPLE 4)========================================
let eps2 = 0.00001
let myfun (x : float) =
    3. * x - 14. + (exp x) - (exp (-x))
let derivativeOfMyFun (x : float) =
    3. + (exp x) + (exp (-x))

let rec getRoot f derivative curX =
    if (abs (f curX) < eps2)
        then curX
        else getRoot f derivative (curX - (f curX) / (derivative curX))
printf "%f\n" (getRoot myfun derivativeOfMyFun 1.)