Предел функции atan(sin(x))/x

Вы ввели

     /atan(sin(x))\
 lim |------------|
x->oo\     x      /

$$\lim_{x \to \infty}\left(\frac{\operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{x}\right)$$

Другие пределы при x→0, -oo, +oo, 1

$$\lim_{x \to \infty}\left(\frac{\operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{x}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{\operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{x}\right) = 1$$

$$\lim_{x \to 0^+}\left(\frac{\operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{x}\right) = 1$$

$$\lim_{x \to 1^-}\left(\frac{\operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{x}\right) = \operatorname{atan}{\left(\sin{\left(1 \right)} \right)}$$

$$\lim_{x \to 1^+}\left(\frac{\operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{x}\right) = \operatorname{atan}{\left(\sin{\left(1 \right)} \right)}$$

$$\lim_{x \to -\infty}\left(\frac{\operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{x}\right) = 0$$

Быстрый ответ

0

$$0$$

График