$\lim\limits_{x \rightarrow-\infty} \frac{x^4 \sin \left(\frac{1}{x}\right)+x^2}{1+|x|^3}$ equals

-1 0 2 1

-1

$\lim\limits_{x \rightarrow-\infty} \frac{\frac{\sin (1 / x)}{1 / x}+\frac{1}{x}}{\frac{1}{x^3}+\frac{|x|^3}{x^3}}=\frac{1-0}{0-1}=-1$ Hence (1) is the correct answer.