What is the limit as x approaches 0+of (-6ln(x))^x ?

The limit as x approaches 0+of (-6ln(x))^x is Does not exist

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limit as x approaches 0+of (-6ln(x))^x

x \to 0 + lim ((- 6 ln (x))^{x})

Does not exist

Solution steps

x \to 0 + lim ((- 6 ln (x))^{x})

Apply exponent rule:

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

(- 6 ln (x))^{x} = (- 1)^{x} (6 ln (x))^{x}

= x \to 0 + lim ((- 1)^{x} (6 ln (x))^{x})

(- 1)^{x} (6 ln (x))^{x}

undefined for

x

approaching

0

from the right

= Does not exist

x \to 1 lim (x^{2} + 2 x + 1)

x \to 4 lim (\frac{- 4 x ^{2} + 16 x}{x ^{3} - 3 x ^{2} - 4 x})

n \to \infty lim ((- 2)^{n})

x \to \infty + lim (sin (x))

x \to 2 - lim (\frac{2 - x}{∣ 2 - x ∣})

What is the limit as x approaches 0+of (-6ln(x))^x ?
The limit as x approaches 0+of (-6ln(x))^x is Does not exist