What is the limit as x approaches 0+of (-4ln(x))^x ?

The limit as x approaches 0+of (-4ln(x))^x is Does not exist

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limit as x approaches 0+of (-4ln(x))^x

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

Does not exist

Solution steps

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

Apply exponent rule:

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

(- 4 ln (x))^{x} = (- 1)^{x} (4 ln (x))^{x}

= x \to 0 + lim ((- 1)^{x} (4 ln (x))^{x})

(- 1)^{x} (4 ln (x))^{x}

undefined for

x

approaching

0

from the right

= Does not exist

x \to 0 lim (\frac{( 1 - x ) ^{4} - 1}{x})

x \to - 4 - lim (x)

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

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

x \to 72 lim (ln (x))

What is the limit as x approaches 0+of (-4ln(x))^x ?
The limit as x approaches 0+of (-4ln(x))^x is Does not exist