Question

Вычислите: __________

Answer 1

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

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

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