What is the limit as x approaches 0+of (-3ln(x))^x ?

The limit as x approaches 0+of (-3ln(x))^x is Does not exist

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limit as x approaches 0+of (-3ln(x))^x

x \to 0 + lim ((- 3 ln (x))^{x})

Does not exist

Solution steps

x \to 0 + lim ((- 3 ln (x))^{x})

Apply exponent rule:

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

(- 3 ln (x))^{x} = (- 1)^{x} (3 ln (x))^{x}

= x \to 0 + lim ((- 1)^{x} (3 ln (x))^{x})

(- 1)^{x} (3 ln (x))^{x}

undefined for

x

approaching

0

from the right

= Does not exist

x \to \frac{5}{2} lim (ln (2 x - 5))

x \to 0.1 lim (\frac{sin ( x )}{x})

x \to e lim (\frac{ln ( x )}{x - e})

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

θ \to \frac{3 π}{2} lim (sin (tan (cos (θ))))

What is the limit as x approaches 0+of (-3ln(x))^x ?
The limit as x approaches 0+of (-3ln(x))^x is Does not exist