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人気のある微分積分 >

limit as x approaches 0 of (ln(cos(x)))/(ln(cos(2x)))

解

x \to 0 lim (\frac{ln ( cos ( x ) )}{ln ( cos ( 2 x ) )})

解

\frac{1}{4}

+1

十進法表記

0.25

解答ステップ

x \to 0 lim (\frac{ln ( cos ( x ) )}{ln ( cos ( 2 x ) )})

ロピタルの定理を適用する

= x \to 0 lim (\frac{- tan ( x )}{- 2 tan ( 2 x )})

ロピタルの定理を適用する

= x \to 0 lim (\frac{- sec ^{2} ( x )}{- 4 sec ^{2} ( 2 x )})

値を挿入する

x = 0

= \frac{- sec ^{2} ( 0 )}{- 4 sec ^{2} ( 2 \cdot 0 )}

簡素化

\frac{- sec ^{2} ( 0 )}{- 4 sec ^{2} ( 2 \cdot 0 )} : \frac{1}{4}

= \frac{1}{4}

グラフ

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