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

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

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

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

0

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

0

= 0

n = 1 \sum \infty \frac{5 ^{n}}{n !}

cos (ln (x))

\int_{0}^{1} \frac{e ^{- 2 x}}{2} d x

x \to 0 lim (sinh (x) cot (x))

n = 0 \sum \infty n x^{n}

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