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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

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n = 0 \sum \infty \frac{n}{3}

\int_{0}^{\frac{π}{2}} cos^{2} (t) d t

x \to 0 + lim (x^{2} + 4)

\int x e^{e} d x

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