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人気のある微分積分 >

limit as x approaches 0 of x(csc(4x))

解

x \to 0 lim (x (csc (4 x)))

解

\frac{1}{4}

+1

十進法表記

0.25

解答ステップ

x \to 0 lim (x csc (4 x))

サイン, コサインで表わす

= x \to 0 lim (\frac{x}{sin ( 4 x )})

ロピタルの定理を適用する

= x \to 0 lim (\frac{1}{cos ( 4 x ) \cdot 4})

値を挿入する

x = 0

= \frac{1}{cos ( 4 \cdot 0 ) \cdot 4}

cos (4 \cdot 0) \cdot 4 = 4

= \frac{1}{4}

グラフ

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