Question

lim (x-кореньx^2
x—>беск. +7х+10)=
Помогите плиз!!!!!!!

Answer 1

$displaystyle lim_{x to infty} (x-sqrt{x^2+7x+10})=\\\=lim_{x to infty} frac{(x-sqrt{x^2+7x+10})(x+sqrt{x^2+7x+10})}{x+sqrt{x^2+7x+10}}=\\\=lim_{x to infty} frac{x^2-(x^2+7x+10)}{x+sqrt{x^2+7x+10}}=lim_{x to infty} frac{-7x-10}{x+sqrt{x^2+7x+10}}=\\\=lim_{x to infty} frac{-frac{7x}x-frac{10}x}{frac{x}x+sqrt{frac{x^2}{x^2}+frac{7x}{x^2}+frac{10}{x^2}}}=frac{-7-0}{1+sqrt{1+0+0}}=-frac{7}{1+1}=-frac{7}2$