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人気のある微分積分 >

limit as x approaches 1-of ln(x)*ln(1-x)

解

x \to 1 - lim (ln (x) \cdot ln (1 - x))

解

0

解答ステップ

x \to 1 - lim (ln (x) ln (1 - x))

ロピタル向けに書き換える

= x \to 1 - lim (\frac{ln ( 1 - x )}{\frac{1}{l n ( x )}})

ロピタルの定理を適用する

= x \to 1 - lim (\frac{- \frac{1}{1 - x}}{- \frac{1}{x l n ^{2} ( x )}})

簡素化

\frac{- \frac{1}{1 - x}}{- \frac{1}{x l n ^{2} ( x )}} : \frac{x ln ^{2} ( x )}{1 - x}

= x \to 1 - lim (\frac{x ln ^{2} ( x )}{1 - x})

ロピタルの定理を適用する

= x \to 1 - lim (\frac{ln ^{2} ( x ) + 2 ln ( x )}{- 1})

値を挿入する

x = 1

= \frac{ln ^{2} ( 1 ) + 2 ln ( 1 )}{- 1}

簡素化

\frac{ln ^{2} ( 1 ) + 2 ln ( 1 )}{- 1} : 0

= 0

グラフ

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