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受欢迎的微积分 >

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

解答

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

解答

0

求解步骤

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

使用指数法则:

a^{n} \cdot b^{n} = (a \cdot b)^{n}

x^{2} ln^{2} (x) = (x ln (x))^{2}

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

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

不定型除外

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

改写以应用洛必达法则

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

使用洛必达法则

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

化简

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

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

代入值

x = 0

= (- 0)^{2}

化简

= 0

作图

流行的例子

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