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人気のある微分積分 >

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

解

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

解

0

解答ステップ

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

ln (x^{3}) = 3 ln (x)

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

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

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

ロピタル向けに書き換える

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

ロピタルの定理を適用する

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

簡素化

\frac{\frac{1}{x}}{- \frac{2}{x ^{3}}} : - \frac{x ^{2}}{2}

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

値を挿入する

x = 0

= 3 (- \frac{0 ^{2}}{2})

簡素化

3 (- \frac{0 ^{2}}{2}) : 0

= 0

グラフ

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