What is the limit as x approaches 0+of (ln(1/x))^x ?

The limit as x approaches 0+of (ln(1/x))^x is 1

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limit as x approaches 0+of (ln(1/x))^x

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

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x \to \infty lim (x^{- x})

\int_{0}^{2} x (x^{2} + 1)^{5} d x

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What is the limit as x approaches 0+of (ln(1/x))^x ?
The limit as x approaches 0+of (ln(1/x))^x is 1