limit as x approaches 0+of (5x^2)(ln(x))

解答

x \to 0 + lim ((5 x^{2}) (ln (x)))

0

求解步骤

x \to 0 + lim (5 x^{2} ln (x))

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

= 5 \cdot x \to 0 + lim (x^{2} ln (x))

改写以应用洛必达法则

= 5 \cdot x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x ^{2}}})

使用洛必达法则

= 5 \cdot x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{2}{x ^{3}}})

化简

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

= 5 \cdot x \to 0 + lim (- \frac{x ^{2}}{2})

代入值

x = 0

= 5 (- \frac{0 ^{2}}{2})

化简

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

= 0

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