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

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

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limit as x approaches 1 of (x-1)^x

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

0

Solution steps

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

Plug in the value

x = 1

= (1 - 1)^{1}

Simplify

= 0

x \to 0 lim (\frac{x}{5 + sin ( x )})

x \to 2 - lim (\frac{10}{x ^{2} - 4})

x \to 0 lim (x cot (π x))

x \to 4 lim (3 x^{2} - 2 x + 6)

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

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