Question

1) lim 3x/sinx

2) lim sin0.5x/sin4x

3) lim sin 12x/tg6x

Answer 1

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