Answer 1

\[\lim_{x \to 0} \left[ \frac{\log \left( 1 + x^3 \right)}{\sin^3 x} \right]\]
\[ = \lim_{x \to 0} \left[ \frac{\log \left( 1 + x^3 \right)}{x^3} \times \frac{x^3}{\sin^3 x} \right]\]
\[ = 1 \times \frac{1}{1^3}\]
\[ = 1\]