1.
$\lim\limits_{x\to -\infty}\dfrac{(x^2+1)(2^2-x+4)}{x^3(3x+1)}$
$=\lim\limits_{x\to -\infty}\dfrac{(1+\dfrac{1}{x^2})(2-\dfrac{1}{x}+\dfrac{4}{x^2}) }{3+\dfrac{1}{x}}$
$=\dfrac{2}{3}$
2.
$\lim\limits_{x\to +\infty}\dfrac{(3x^2+1)(2-x^3)}{(2x^4+x)(x+1)}$
$=\lim\limits_{x\to +\infty}\dfrac{(3+\dfrac{1}{x^2})(\dfrac{2}{x^3}-1) }{(2+\dfrac{1}{x^3})(1+\dfrac{1}{x}) }$
$=\dfrac{-3}{2}$