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人気のある微分積分 >

limit as x approaches 0+of x^2ln(2x^3)

解

x \to 0 + lim (x^{2} ln (2 x^{3}))

解

0

解答ステップ

x \to 0 + lim (x^{2} ln (2 x^{3}))

ロピタル向けに書き換える

= x \to 0 + lim (\frac{ln ( 2 x ^{3} )}{\frac{1}{x ^{2}}})

ロピタルの定理を適用する

= x \to 0 + lim (\frac{\frac{3}{x}}{- \frac{2}{x ^{3}}})

簡素化

\frac{\frac{3}{x}}{- \frac{2}{x ^{3}}} : - \frac{3 x ^{2}}{2}

= x \to 0 + lim (- \frac{3 x ^{2}}{2})

値を挿入する

x = 0

= - \frac{3 \cdot 0 ^{2}}{2}

簡素化

= 0

グラフ

人気の例

limit as x approaches 0 of ln(1-e^{-x})

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