1) lim 3x/sinx 2) lim sin0.5x/sin4x 3) lim sin 12x/tg6x

Решите задачу:

$\lim_{x \to 0}\cfrac{3x}{\sin x}= \lim_{x \to 0}\cfrac{3x}{\cfrac{\sin x}{x}\cdot x}= \lim_{x \to 0} 3=3\\ \lim_{x \to 0}\cfrac{\sin 0,5x}{\sin 4x}= \lim_{x \to 0} \cfrac{\cfrac{\sin 0,5 x}{0,5x}\cdot 0,5x}{\cfrac{\sin 4x}{4x}\cdot 4x}=\cfrac{1}{8}\\ \lim_{x \to 0} \cfrac{\sin 12x}{\tan 6x}=\lim_{x\to 0}\cfrac{\cfrac{\sin 12 x}{12x}\cdot 12x\cos x}{\cfrac{\sin 6x}{6x}\cdot 6x}=\lim_{x\to 0} 2\cos x=2$