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人気のある微分積分 >

limit as x approaches 0+of xln(x^8)

解

x \to 0 + lim (x ln (x^{8}))

解

0

解答ステップ

x \to 0 + lim (x ln (x^{8}))

ln (x^{8}) = 8 ln (x)

= x \to 0 + lim (x \cdot 8 ln (x))

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

= 8 \cdot x \to 0 + lim (x ln (x))

ロピタル向けに書き換える

= 8 \cdot x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x}})

ロピタルの定理を適用する

= 8 \cdot x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}})

簡素化

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

= 8 \cdot x \to 0 + lim (- x)

値を挿入する

x = 0

= 8 (- 0)

簡素化

= 0

グラフ

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