Question

Помогите с решением lim 4x/tgП(х+2) x-0

Answer 1

$\displaystyle \lim_{x \to 0}\frac{4x}{{\rm tg}(\pi(x+2))}=\lim_{x \to 0}\frac{(4x)'}{({\rm tg}(\pi (x+2)))'}=\lim_{x \to 0}\frac{4}{\pi/\cos^2(\pi(x+2))}=\\ \\ \\ =\frac{4}{\pi}\lim_{x \to 0}\cos^2(\pi(x+2))=\frac{4}{\pi}\cos^22\pi =\frac{4}{\pi}$