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

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

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limit as x approaches 1+of (x-1)^{(x-1)}

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

(1 - 1)^{1} (1 - 1)^{- 1}

Solution steps

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

Simplify

(x - 1)^{x - 1} : (x - 1)^{x} (x - 1)^{- 1}

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

Plug in the value

x = 1

= (1 - 1)^{1} (1 - 1)^{- 1}

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