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人気のある微分積分 >

limit as x approaches 0 of (tan^2(4x))/(1-cos(5x))

解

x \to 0 lim (\frac{tan ^{2} ( 4 x )}{1 - cos ( 5 x )})

解

\frac{32}{25}

+1

十進法表記

1.28

解答ステップ

x \to 0 lim (\frac{tan ^{2} ( 4 x )}{1 - cos ( 5 x )})

ロピタルの定理を適用する

= x \to 0 lim (\frac{8 sec ^{2} ( 4 x ) tan ( 4 x )}{5 sin ( 5 x )})

ロピタルの定理を適用する

= x \to 0 lim (\frac{8 ( 8 sec ^{2} ( 4 x ) tan ^{2} ( 4 x ) + 4 sec ^{4} ( 4 x ) )}{25 cos ( 5 x )})

値を挿入する

x = 0

= \frac{8 ( 8 sec ^{2} ( 4 \cdot 0 ) tan ^{2} ( 4 \cdot 0 ) + 4 sec ^{4} ( 4 \cdot 0 ) )}{25 cos ( 5 \cdot 0 )}

簡素化

\frac{8 ( 8 sec ^{2} ( 4 \cdot 0 ) tan ^{2} ( 4 \cdot 0 ) + 4 sec ^{4} ( 4 \cdot 0 ) )}{25 cos ( 5 \cdot 0 )} : \frac{32}{25}

= \frac{32}{25}

グラフ

人気の例

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