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

The limit as x approaches 0+of [-ln(x)]^x is Does not exist

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limit as x approaches 0+of [-ln(x)]^x

x \to 0 + lim ([- ln (x)]^{x})

Does not exist

Solution steps

x \to 0 + lim ([- ln (x)]^{x})

Apply exponent rule:

(a \cdot b)^{n} = a^{n} \cdot b^{n}

[- ln (x)]^{x} = (- 1)^{x} (ln (x))^{x}

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

(- 1)^{x} ln^{x} (x)

undefined for

x

approaching

0

from the right

= Does not exist

x \to 1 lim (\frac{2 + x}{1 - x})

x \to 0 lim (x^{4} - 4 ln (x))

x \to 0 lim (\frac{x - 0}{x})

x \to \infty lim (+ x \cdot 0)

x \to 1 lim (x^{- 1} - 1)

What is the limit as x approaches 0+of [-ln(x)]^x ?
The limit as x approaches 0+of [-ln(x)]^x is Does not exist