Question

Номер 9 : О) П) Р) С)

Answer 1

$1); ; limlimits _{x to 0} frac{sin7x}{x}=limlimits _{x to 0}(underbrace {frac{sin7x}{7x}}_{1}cdot 7x)=7cdot 0=0\\2); ; limlimits _{x to 0} frac{x^2}{sqrt{x^2+4}-2} =limlimits _{x to 0}frac{x^2(sqrt{x^2+4}+2)}{x^2+4-4}= limlimits _{x to 0}frac{1}{sqrt{x^2+4}+2}= frac{1}{2+2}=frac{1}{4}\\3); ; limlimits _{x to 5}(x-5)(x^2+5x+25)=0cdot 75=0\\4); ; limlimits _{x to 2}frac{x^2-5x+6}{x^2-6x+8}= limlimits _{x to 2}frac{(x-2)(x-3)}{(x-2)(x-4)}=limlimits _{x to 2}frac{x-3}{x-4}=frac{2-3}{2-4}=frac{1}{2}$