Question

Solve
${lim}_{x\to 0}\frac{\log (1+x^3)}{{\sin }^{3}x}$

Answer 1

$\underset{x\to 0}{lim}\frac{\log (1+x^3)}{\sin 3x}$

$=\underset{x\to 0}{lim}\frac{\frac{\log (1+x^3)}{x3}}{\frac{{\sin }^{3}x}{x^3}}$

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

$=1/1=1$