1. **State the problem:** We want to find the limit $$\lim_{x \to 0} \frac{\sin x - \sin x \cos x}{x^3}$$. 2. **Rewrite the expression:** Factor out $\sin x$ in the numerator: $$\frac{\sin x (1 - \cos x)}{x^3}$$. 3. **Recall important limits and approximations:** - As $x \to 0$, $\sin x \approx x$. - As $x \to 0$, $1 - \cos x \approx \frac{x^2}{2}$. 4. **Substitute approximations:** $$\frac{\sin x (1 - \cos x)}{x^3} \approx \frac{x \cdot \frac{x^2}{2}}{x^3} = \frac{\frac{x^3}{2}}{x^3} = \frac{1}{2}$$. 5. **Conclusion:** Therefore, $$\lim_{x \to 0} \frac{\sin x - \sin x \cos x}{x^3} = \frac{1}{2}.$$