Question

Вычислите
$displaystylelim_{xrightarrowinfty}frac{3x-1}{x^2+7x+5};\ lim_{xrightarrow0,5}(2arcsin x+3arccos x).$

Answer 1

$limlimits _{x to infty} frac{3x-1}{x^2+7x+5} = limlimits _{x to infty} frac{frac{3}{x}-frac{1}{x^2}}{1+frac{7}{x}+frac{5}{x^2}} =frac{0}{1}=0\\ limlimits _{x to 0,5} (2arcsinx+3arccosx)= limlimits _{x to 0,5} (2arcsin0,5+3arccos0,5)=\\=2cdot frac{pi}{6}+3cdot frac{pi}{3}=frac{pi}{3}+pi=frac{4pi}{3}$