x0 = -2; x1 = -1.5; x2 = -1

P0[x_] = (x - 
            x1) (x - x2)/((x0 - x1) (x0 - x2))

P1[x_] = (x - 
            x0) (x - x2)/((x1 - x0) (x1 - x2))

P2[x_] = (x - 
            x0) (x - x1)/((x2 - x0) (x2 - x1))

P[x_] := 7*P0[x] + 4.75*P1[x] + 3*P2[x]

P[-1.2]

Exp[-1]/
        6*(-1.2 + 2) (-1.2 + 1.5) (-1.2 + 
          1)

\(A\ diferença\ de\ terceira\ ordem\ de\ f, \ 
    por\ definição, \ é\ o\ coeficiente\ do\ termo\ principal\ do\ polinómio\ interpolador\ de\ 3  º\ gau, \ 
    neste\ caso, \ f[0, 1, 2, 2.5] = \(\(0.4\)\(.\)\)\)

F0[x_] := x - 1

F1[x_] := (x - 2)^2

x[1] = -1;  x[2] = 0; x[3] = 1

f[1] := 3; f[2] = -1; f[3] = 3

a11 = (∑_(i = 1)^3) F0[x[i]]^2

a12 = (∑_(i = 1)^3) F0[x[i]] F1[x[i]]

a22 = (∑_(i = 1)^3) F1[x[i]]^2

A = {{a11, a12}, {a12, a22}}

b1 = (∑_(i = 1)^3) F0[x[i]] f[i]

b2 = (∑_(i = 1)^3) F1[x[i]] f[i]

b = {b1, b2}

LinearSolve[A, b]

g[x_] = 41/3 (x - 1) + 10/3 (x - 2)^2

h = 2

S = h/3 (-2*7 + 0 + 2*9)

h = 1

S = h/3 (7 + 4*4.75 + 0 + 4*3 + 9)

f[x_, y_] :=  y^2 + x*y

y1 = y0 + h*f[x0, y0]

y1 = 
      y0 + h*f[x0, y0] +  
        h^2/2*(y0 + (2  y0 + x0)*f[x0, y0])

\(1  º\ passo\)

x0 = 0; y0 = 1; h = 0.1

y1 = y0 + h*f[x0, y0]

\(2  º\ passo\)

x1 = 0.1

y2 = y1 + h*f[x1, y1]