limit as x approaches 0+of sqrt(x)ln(x)

解答

x \to 0 + lim (x ln (x))

0

求解步骤

x \to 0 + lim (x ln (x))

改写以应用洛必达法则

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

使用洛必达法则

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

化简

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

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

代入值

x = 0

= - 2 \cdot 0^{\frac{1}{2}}

化简

= 0

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