Question

Найти предел функции $lim_{x to 0} cos(3x)-1/(x*tg(2x))$

Answer 1

$displaystyle lim_{x to 0} frac{sinx}{x}=1; lim_{x to 0} frac{tgx}{x}=1; 1-cosx=2sin^2(x/2);\lim_{x to 0} frac{cos(3x)-1}{xtg(2x)}=lim_{x to 0} frac{cos(3x)-1}{x*2x}=\lim_{x to 0} frac{-2sin(3frac{x}{2})^2}{2x^2}=lim_{x to 0} frac{-9frac{x^2}{4}}{x^2}=lim_{x to 0} frac{-9x^2}{4x^2}=-frac{9}{4};$