Question

Помогите,пожалуйста))

Answer 1

$limlimits _{x to 1} frac{x^2+4}{x-2} = frac{1+4}{1-2} =-5\\limlimits _{xto 1} frac{x^2-1}{x^2-5x+4} =limlimits _{xto 1} frac{(x-1)(x+1)}{(x-1)(x-4)} =limlimits _{xto 1} frac{x+1}{x-4} =-frac{2}{3}\\limlimits_{xto infty } frac{5x-2}{x^2-x+4} =limlimits _{xto infty } frac{frac{5}{x}-frac{2}{x^2}}{1-frac{1}{x}+frac{4}{x^2}} = frac{0}{1}=0$

$limlimits _{xto infty } frac{x^3+4}{x^2-3} =limlimits _{xto infty } frac{1+frac{4}{x^3}}{frac{1}{x}-frac{3}{x^3}} =frac{1}{0}=infty$

$lim_{x to infty} frac{x^2+4x-5}{x^2-1} = lim_{x to infty}frac{1+frac{4}{x}-frac{5}{x^2}}{1-frac{1}{x^2}} =frac{1}{1}=1\\\limlimits _{alpha (x)to 0}, frac{1}{alpha (x)}=infty ; ; ;; ; ; limlimits _{alpha (x)to infty }, frac{1}{alpha (x)}=0$