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

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

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

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

- 1

Solution steps

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

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

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

x \to 0 + lim (1) = 1

= 0 - 1

Simplify

= - 1

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

x \to 3 - lim (\frac{x}{9 - x ^{2}})

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