limit as x approaches infinity of arctan(5)-arctan(x+1)

解

x \to \infty lim (arctan (5) - arctan (x + 1))

arctan (5) - \frac{π}{2}

十進法表記

- 0.19739 \dots

解答ステップ

x \to \infty lim (arctan (5) - arctan (x + 1))

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

不定形式の場合を除く

= x \to \infty lim (arctan (5)) - x \to \infty lim (arctan (x + 1))

x \to \infty lim (arctan (5)) = arctan (5)

x \to \infty lim (arctan (x + 1)) = \frac{π}{2}

= arctan (5) - \frac{π}{2}