limit as x approaches 0+of x^{12}*ln(x)

解答

x \to 0 + lim (x^{12} \cdot ln (x))

0

求解步骤

x \to 0 + lim (x^{12} ln (x))

改写以应用洛必达法则

= x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x ^{12}}})

使用洛必达法则

= x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{12}{x ^{13}}})

化简

\frac{\frac{1}{x}}{- \frac{12}{x ^{13}}} : - \frac{x ^{12}}{12}

= x \to 0 + lim (- \frac{x ^{12}}{12})

代入值

x = 0

= - \frac{0 ^{12}}{12}

化简

- \frac{0 ^{12}}{12} : 0

= 0

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