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

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

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limit as x approaches 0+of (x^x)^x

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

x \to 5 - lim ((x - 5) \cdot ln (5 - x))

z \to 1 lim (\frac{x + y - 1}{z - 1})

x \to 2 lim (\frac{∣ x + 2 ∣}{x + 2})

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

n \to \infty lim (\frac{( sin ( n ) )}{n})

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