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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

\frac{d}{d x} (x^{2} x^{4} - 12)

\frac{d y}{d x} = \frac{( 3 x ^{2} )}{y ^{2}}

\frac{d}{d x} (x - sin (2 x))

x \to - 2 lim (x (2))

\frac{\partial}{\partial y} (2 e^{x})

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