How to solve this limit without L'Hospital's Rule?

Question

I am new to this site, so I don't know if this will appear correctly.

I need to solve this limit without L'Hospital's Rule:

$$ \lim_{x\to 0}\frac{x-\sin x}{x^3}.$$

I know that the result is $\frac{1}{6}$ but I need a step-by-step solution.

Thanks in advance.

Answer 1

HINT Expand $\sin x$ into Taylor series around 0