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

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

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

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

0

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

0

= 0

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