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人気のある微分積分 >

limit as x approaches infinity of pi/2 arctan(x)

解

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

解

\frac{π ^{2}}{4}

+1

十進法表記

2.46740 \dots

解答ステップ

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

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

= \frac{π}{2} \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{π}{2} \cdot \frac{π}{2}

簡素化

\frac{π}{2} \cdot \frac{π}{2} : \frac{π ^{2}}{4}

= \frac{π ^{2}}{4}

グラフ

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