Problems from Indeterminate form infinity/infinity

Development:

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

Solution:

$$\dfrac{1}{6}$$

Hide solution and development

Development:

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

Solution:

a) $$-\infty$$

b) $$-\infty$$

Hide solution and development