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

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

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

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

0

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

0

= 0

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

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

x \to 8 - lim (\frac{- 7}{x ^{2} - 8 x})

x \to 0 lim (1 + 2 x)

x \to 0 lim (3 x csc (x))

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