Предел функции x*atan(1/x)

Другие пределы при x→0, -oo, +oo, 1

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

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

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

$$\lim_{x \to 1^-}\left(x \operatorname{atan}{\left(\frac{1}{x} \right)}\right) = \frac{\pi}{4}$$

$$\lim_{x \to 1^+}\left(x \operatorname{atan}{\left(\frac{1}{x} \right)}\right) = \frac{\pi}{4}$$

Быстрый ответ

1

$$1$$

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