Question

$\underset{x\to 0}{\lim }\frac{\log \left|1+x^3\right|}{{\sin }^{3}x}$

Answer 1

$$\begin{gathered} \underset{x\to 0}{\lim }\left[\frac{\log \left(1+x^3\right)}{{\sin }^{3}x}\right] \\ =\underset{x\to 0}{\lim }\left[\frac{\log \left(1+x^3\right)}{x^3}\times \frac{x^3}{{\sin }^{3}x}\right] \\ =1\times \frac{1}{1^3} \\ =1 \end{gathered}$$