Question

помогите....
Вычислите предел
$lim_{x to infty}(6 frac{4-2 x^{2} }{4 x^{2}+3 }-3 frac{x+ x^{2}+4 x^{4} }{2 x^{4}+10})$

Answer 1

$lim_{xtoinfty}(frac{24-12x^2}{4x^2+3}-frac{3x+3x^2+4x^4}{2x^4+10})=lim_{xtoinfty}(frac{-12x^2}{4x^2}-frac{x(3+3x+4x^3)}{2x^4})=\=-3-lim_{xtoinfty}frac{3+3x+4x^3}{2x^3}=3-lim_{xtoinfty}frac{x(3+4x^2)}{2x^3}=\=3-lim_{xtoinfty}frac{3+4x^2}{2x^2}=3-lim_{xtoinfty}frac{4x^2}{2x^2}=3-2=1$