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

x \to 0 lim (\frac{2 x + 3}{2 x - 1})

x \to 3 lim (5 - 2 x)

x \to 4 lim (3 - 5 + x)

y \to 0 lim (cot (y) - csc (y))

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

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