Question

Вычислите: __________

Answer 1

"sin(ax)" эквивалентен "ax" при x --> 0

"tg(ax)" эквивалентен "ax" при x --> 0

$1.lim_{x to 0} frac{5x}{sin5x} =lim_{x to 0} frac{5x}{5x} =lim_{x to 0} 1 =1 \ \ 2. lim_{x to 0} frac{sin3x}{2x} =lim_{x to 0} frac{3x}{2x} =lim_{x to 0} frac{3}{2} =frac{3}{2} \ \ 3. lim_{x to 0} frac{tg5x}{sinx} =lim_{x to 0} frac{5x}{x} =lim_{x to 0} 5 =5 \ \ 4. lim_{x to 0} frac{tg2x}{sin5x} =lim_{x to 0} frac{2x}{5x} =lim_{x to 0} frac{2}{5}=frac{2}{5}$