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人気のある微分積分 >

limit as x approaches infinity of 1/(arctan(sqrt(x)))

解

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

解

\frac{2}{π}

+1

十進法表記

0.63661 \dots

解答ステップ

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

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

不定形式の場合を除く

= \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( arctan ( x ) )}

x \to \infty lim (1) = 1

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

= \frac{1}{\frac{π}{2}}

簡素化

= \frac{2}{π}

グラフ

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