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

The limit as x approaches 1 of (x^{-x}-1)/x is 0

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

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

0

Solution steps

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

Plug in the value

x = 1

= \frac{1 ^{- 1} - 1}{1}

Simplify

= 0

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

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

x \to 5 lim (3 x + 1)

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

x \to - 2 lim (2 x^{3} - x^{2} + 4 x + 1)

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