What is the limit as x approaches 0+of x^{x-1} ?

The limit as x approaches 0+of x^{x-1} is infinity

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limit as x approaches 0+of x^{x-1}

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

\infty

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

\infty

= \infty

x \to 3 lim (\frac{x}{0})

x \to 2 lim (3 x^{2} - 3 x + 11)

x \to 0 - lim (\frac{2}{1 - 2 ^{\frac{1}{x}}})

x \to 2 lim (7 x^{2} + 3 x - 40)

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

What is the limit as x approaches 0+of x^{x-1} ?
The limit as x approaches 0+of x^{x-1} is infinity