LIM (x tends to 0) ((e ^ x) * sinx-x (1 + x)) / x ^ 3 is solved by Taylor's theorem

LIM (x tends to 0) ((e ^ x) * sinx-x (1 + x)) / x ^ 3 is solved by Taylor's theorem

Expanding e ^ x SiNx with Taylor formula
e^x=1+x+x²/2+o(x³)
sinx=x-x³/6+o(x³)
The limit is 1 / 3