Indeterminate form infinity/infinity

Find the following limits:

a) $\displaystyle\lim_{x \to{+}\infty}{\dfrac{-x^2+x+log x}{3x}}$

b) $\displaystyle\lim_{x \to{-}\infty}{\dfrac{x^3+3}{x}}$

a) $\displaystyle\lim_{x \to{+}\infty}{\dfrac{-x^2+x+log x}{3x}}=\lim_{x \to{+}\infty}{\dfrac{-x^2}{3x}}=-(+\infty)^2=-\infty$

b) $\displaystyle\lim_{x \to{-}\infty}{\dfrac{x^3+3}{x}}=\lim_{x \to{-}\infty}{x^3}=(-\infty)^3=-\infty$

a) $-\infty$

b) $-\infty$

Find the following limit:

$$\displaystyle\lim_{x \to{+}\infty}{\dfrac{\frac{1}{2}x+56}{3x+1}}$$

$$\displaystyle\lim_{x \to{+}\infty}{\dfrac{\frac{1}{2}x+56}{3x+1}}=\dfrac{\frac{1}{2}x}{3x}=\dfrac{\frac{1}{2}}{3}=\dfrac{1}{6}$$

$\dfrac{1}{6}$