l0[x_]:=((x-0.5)(x-1)(x-1.5))/((0-0.5)(0-1)(0-1.5))

l1[x_]:=((x-0)(x-1)(x-1.5))/((0.5-0)(0.5-1)(0.5-1.5))

l2[x_]:=((x-0)(x-0.5)(x-1.5))/((1-0)(1-0.5)(1-1.5))

l3[x_]:=((x-0)(x-0.5)(x-1))/((1.5-0)(1.5-0.5)(1.5-1))

ln[x]=l0[x]*1+l1[x]*2+l2[x]*3+l3[x]*4

Simplify[ln[x]]

Solve[{a 0^3+b 0^2+c 0+d==1,a 0.5^3+b 0.5^2+c 0.5+d==2, a 1^3+b 1^2+c 1+d==3, a 1.5^3+b 1.5^2+c 1.5+d==4},{a,b,c,d}]

p[x_]=[((x-0.1)(x-0.2)(x-0.3))/((0-0.1)(0-0.2)(0-0.3)),((x-0)(x-0.2)(x-0.3))/((0.1-0)(0.1-0.2)(0.1-0.3)),
((x-0)(x-0.1)(x-0.3))/((0.2-0)(0.2-0.1)(0.2-0.3)),((x-0)(x-0.1)(x-0.2))/((0.3-0)(0.3-0.1)(0.3-0.1))]

p0[x_]=((x-0.1)(x-0.2)(x-0.3))/((0-0.1)(0-0.2)(0-0.3))

-166.66666666666663` (-0.3`+x) (-0.2`+x) (-0.1`+x)
Solve[E^0]

E^0

E^0.1

E^0.2

E^0.3

r0 [x_]:=((x-0.1)(x-0.2)(x-0.3))/((0-0.1)(0-0.2)(0-0.3))
r1[x_]:=((x-0)(x-0.2)(x-0.3))/((0.1-0)(0.1-0.2)(0.1-0.3))
r2[x_]:=((x-0)(x-0.1)(x-0.3))/((0.2-0)(0.2-0.1)(0.2-0.3))
r3[x_]:=((x-0)(x-0.1)(x-0.2))/((0.3-0)(0.3-0.1)(0.3-0.1))

r[x_]=1*r0[x]+1.10517*r1[x]+1.2214*r2[x]+1.34986*r3[x]

Simplify[r[x]]

%/.x->0.15

4!

greshka[x_]=(E^x/4!)(0.15-0)(0.15-0.1)(0.15-0.2)(0.15-0.3)

%/.x->0.15

N[%70]-N[%58]

greshka[0]

greshka[0.3]

N[%65]-N[%58]