Question

Помогите найти пределы.

Answer 1

$displaystyle lim_{xto-1}frac{7x^2+8x+1}{2x+2}=frac{0}{0}=lim_{xto-1}frac{(x+1)(7x+1)}{2(x+1)}=lim_{xto-1}frac{7x+1}{2}=-3$

$displaystyle lim_{xtoinfty}(x-sqrt{x^2+3x})=infty-infty=displaystyle lim_{xtoinfty}frac{-3x}{(x+sqrt{x^2+3x})}=frac{infty}{infty}=\=lim_{xtoinfty}frac{-3x}{x(1+sqrt{1+frac{3}{x}_{to0}})}=-frac{3}{2}$

$displaystyle lim_{xto0}frac{tg6x}{tg3x}=frac{0}{0}=lim_{xto0}frac{6x}{3x}=2$

$displaystyle lim_{xtoinfty}(frac{5x+2}{5x-3})^{2x+1}=1^infty=lim_{xtoinfty}(frac{5x-3+5}{5x-3})^{2x+1}=\=[lim_{xtoinfty}(1+frac{5}{5x-3})^frac{5x-3}{5}]^{frac{5(2x+1)}{5x-3}}=e^{displaystyle5lim_{xtoinfty}frac{2x+1}{5x-3}}=e^2$