Question

нужна ваша помощь, премного благодарен​

Answer 1

Ответ:

$1)\ \ \lim\limits _{x \to -5}\dfrac{\sqrt{20-x}+x}{x^2-25}=\lim\limits _{x \to -5}\dfrac{(20-x)-x^2}{(x-5)(x+5)(\sqrt{20-x}-x)}=\\\\\\=\lim\limits _{x \to -5}\dfrac{-(x-4)(x+5)}{(x-5)(x+5)(\sqrt{20-x}-x)}=\lim\limits _{x \to -5}\dfrac{-(x-4)}{(x-5)(\sqrt{20-x}-x)}=\\\\=\dfrac{9}{-100}=-0,09$

$2)\ \ y=\dfrac{7}{x^2-1}\ \ \ ,\ \ \ y'=\dfrac{-7\cdot 2x}{(x^2-1)^2}=-\dfrac{14x}{(x^2-1)^2}\\\\\\3)\ \ \int \dfrac{dx}{cos^2\frac{7x}{2}}=\dfrac{2}{7}\cdot tg\dfrac{7x}{2}+C$