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인기 있는 미적분학 >

limit as x approaches 0+of x(ln(x))^6

해법

x \to 0 + lim (x (ln (x))^{6})

해법

0

솔루션 단계

x \to 0 + lim (x (ln (x))^{6})

L'Hopital을 위해 다시 쓰기

= x \to 0 + lim (\frac{( ln ( x ) ) ^{6}}{\frac{1}{x}})

L'Hopital 의 규칙 적용

= x \to 0 + lim (\frac{\frac{6 l n ^{5} ( x )}{x}}{- \frac{1}{x ^{2}}})

\frac{\frac{6 l n ^{5} ( x )}{x}}{- \frac{1}{x ^{2}}}

단순화하세요:

- 6 x ln^{5} (x)

= x \to 0 + lim (- 6 x ln^{5} (x))

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

= - 6 \cdot x \to 0 + lim (x ln^{5} (x))

L'Hopital을 위해 다시 쓰기

= - 6 \cdot x \to 0 + lim (\frac{ln ^{5} ( x )}{\frac{1}{x}})

L'Hopital 의 규칙 적용

= - 6 \cdot x \to 0 + lim (\frac{\frac{5 l n ^{4} ( x )}{x}}{- \frac{1}{x ^{2}}})

\frac{\frac{5 l n ^{4} ( x )}{x}}{- \frac{1}{x ^{2}}}

단순화하세요:

- 5 x ln^{4} (x)

= - 6 \cdot x \to 0 + lim (- 5 x ln^{4} (x))

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

= - 6 (- 5 \cdot x \to 0 + lim (x ln^{4} (x)))

L'Hopital을 위해 다시 쓰기

= - 6 (- 5 \cdot x \to 0 + lim (\frac{ln ^{4} ( x )}{\frac{1}{x}}))

L'Hopital 의 규칙 적용

= - 6 (- 5 \cdot x \to 0 + lim (\frac{\frac{4 l n ^{3} ( x )}{x}}{- \frac{1}{x ^{2}}}))

\frac{\frac{4 l n ^{3} ( x )}{x}}{- \frac{1}{x ^{2}}}

단순화하세요:

- 4 x ln^{3} (x)

= - 6 (- 5 \cdot x \to 0 + lim (- 4 x ln^{3} (x)))

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

= - 6 (- 5 (- 4 \cdot x \to 0 + lim (x ln^{3} (x))))

L'Hopital을 위해 다시 쓰기

= - 6 (- 5 (- 4 \cdot x \to 0 + lim (\frac{ln ^{3} ( x )}{\frac{1}{x}})))

L'Hopital 의 규칙 적용

= - 6 (- 5 (- 4 \cdot x \to 0 + lim (\frac{\frac{3 l n ^{2} ( x )}{x}}{- \frac{1}{x ^{2}}})))

\frac{\frac{3 l n ^{2} ( x )}{x}}{- \frac{1}{x ^{2}}}

단순화하세요:

- 3 x ln^{2} (x)

= - 6 (- 5 (- 4 \cdot x \to 0 + lim (- 3 x ln^{2} (x))))

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

= - 6 (- 5 (- 4 (- 3 \cdot x \to 0 + lim (x ln^{2} (x)))))

L'Hopital을 위해 다시 쓰기

= - 6 (- 5 (- 4 (- 3 \cdot x \to 0 + lim (\frac{ln ^{2} ( x )}{\frac{1}{x}}))))

L'Hopital 의 규칙 적용

= - 6 (- 5 (- 4 (- 3 \cdot x \to 0 + lim (\frac{\frac{2 l n ( x )}{x}}{- \frac{1}{x ^{2}}}))))

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

단순화하세요:

- 2 x ln (x)

= - 6 (- 5 (- 4 (- 3 \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)

= - 6 (- 5 (- 4 (- 3 (- 2 \cdot x \to 0 + lim (x ln (x))))))

L'Hopital을 위해 다시 쓰기

= - 6 (- 5 (- 4 (- 3 (- 2 \cdot x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x}})))))

L'Hopital 의 규칙 적용

= - 6 (- 5 (- 4 (- 3 (- 2 \cdot x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}})))))

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

단순화하세요:

- x

= - 6 (- 5 (- 4 (- 3 (- 2 \cdot x \to 0 + lim (- x)))))

Plug in the value

x = 0

= - 6 (- 5 (- 4 (- 3 (- 2 (- 0)))))

단순화

= 0

그래프

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