Question

Номер 9 : О) П) Р) С)

Answer 1

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