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人気のある微分積分 >

limit as x approaches 0 of 8xcsc(9x)

解

x \to 0 lim (8 x csc (9 x))

解

\frac{8}{9}

+1

十進法表記

0.88888 \dots

解答ステップ

x \to 0 lim (8 x csc (9 x))

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

= 8 \cdot x \to 0 lim (x csc (9 x))

サイン, コサインで表わす

= 8 \cdot x \to 0 lim (\frac{x}{sin ( 9 x )})

ロピタルの定理を適用する

= 8 \cdot x \to 0 lim (\frac{1}{cos ( 9 x ) \cdot 9})

値を挿入する

x = 0

= 8 \cdot \frac{1}{cos ( 9 \cdot 0 ) \cdot 9}

簡素化

8 \cdot \frac{1}{cos ( 9 \cdot 0 ) \cdot 9} : \frac{8}{9}

= \frac{8}{9}

グラフ

人気の例

limit as x approaches 2 of (x-1)/(x^3-1)

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