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

解答

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

解答

0

求解步骤

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

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

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

改写以应用洛必达法则

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

使用洛必达法则

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

化简

\frac{\frac{2 l n ( x )}{x}}{- \frac{1}{x ^{2}}} : - 2 x ln (x)

= 2 \cdot x \to 0 + lim (- 2 x ln (x))

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

= 2 (- 2 \cdot x \to 0 + lim (x ln (x)))

改写以应用洛必达法则

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

使用洛必达法则

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

化简

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

= 2 (- 2 \cdot x \to 0 + lim (- x))

代入值

x = 0

= 2 (- 2 (- 0))

化简

= 0

作图

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