L[x_] := 10  (((x-121)(x-144))/((100-121)(100-144)))+11 (((x-100)(x-144))/((121-100)(121-144)))+12(((x-100)(x-121))/((144-100)(144-121)))

L[x]

Expand[(5/462) (-144+x) (-121+x)-(11/483) (-144+x) (-100+x)+(3/253) (-121+x) (-100+x)]

FullSimplify[(5/462) (-144+x) (-121+x)-(11/483) (-144+x) (-100+x)+(3/253) (-121+x) (-100+x)]

L[147.5]

Expand[L[x]]

L[147.5]

L[115]

L[115.]

Истинска Грешка

y[x_] := (Sqrt[x])

y[115]

y[115.]

L[115.] - y[115.]

Извод : Истинската грешка е  0.00104979

Теоритична Грешка

Plot[Abs[y'''[x]],{x,100,144}]

M3 = Abs[y'''[100]]

R[x_] := (M3/(3!))Abs[(x-100)(x-121)(x-144)]

R[115.]

1) Смятаме Полинома

L[147.5]

Намерената стойност на полинома в 147.5 е  12.14
Истинска Грешка

y[147.5]

L[147.5] - y[147.5]

Теоритична Грешка

Plot[Abs[y'''[x]],{x,100,147.5}]

M3 = Abs[y'''[100]]

R[x_] := (M3/(3!))Abs[(x-100)(x-121)(x-144)]

R[147.5]

L[147.5] - y[147.5]

L[1]

% // N

e = 3.1677;

Plot[Abs[y'''[x]], {x, 1, 144}]

Plot[Abs[y'''[x]], {x, 1, 20}]

x= .

Plot[Abs[y'''[x]], {x, 1, 10}]

Abs[y'''[1]] // N

M3 = Abs[y'''[1]]

x= 3/8

(M3/(3!))Abs[(1-100)(1-121)(1-144)]

%//N

x=Table[3+0.1*k,{k,-3,7}]

f[x_]:=Cos[(E^(π*x))+2]-3
f[x]