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

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

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

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

0

Solution steps

x \to 0 + lim (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 \to 0 + lim (1)

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

x \to 0 + lim (1) = 1

= 1 - 1

Simplify

= 0

\frac{d}{d x} (- 2 e^{- x} x)

sin (4 x)

\frac{\partial}{\partial x} (\frac{1}{3 x})

x \to 1 + lim ((x - 1) ∣ x - 1 ∣)

\int cos (π) x d x

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