limit as x approaches-infinity of 1/9 arctan(x)

解

x \to - \infty lim (\frac{1}{9} arctan (x))

- \frac{π}{18}

十進法表記

- 0.17453 \dots

解答ステップ

x \to - \infty lim (\frac{1}{9} arctan (x))

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{9} \cdot x \to - \infty lim (arctan (x))

共通限度を適用する:

x \to - \infty lim (arctan (x)) = - \frac{π}{2}

= \frac{1}{9} (- \frac{π}{2})

簡素化

\frac{1}{9} (- \frac{π}{2}) : - \frac{π}{18}

= - \frac{π}{18}