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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

\frac{d}{d x} (10 cos (\frac{3}{10} x))

n = 3 \sum \infty \frac{n + 7}{n !}

\int (sin (x) cos (x))^{4} d x

f (x) = x^{2} + 8 x

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

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