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

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

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limit as x approaches 0+of x^x

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

\frac{\partial}{\partial x} (x^{6} - 8 x^{3} y)

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n = 0 \sum \infty (\frac{1}{3})^{n - 1}

\frac{\partial}{\partial x} (9 e^{x} x)

\frac{d}{d x} ((2 x - 1) (x + 3))

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