What is the limit as x approaches 2 of (x-2)^{(x-2)} ?

The limit as x approaches 2 of (x-2)^{(x-2)} is Does not exist

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limit as x approaches 2 of (x-2)^{(x-2)}

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

Does not exist

Solution steps

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

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

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

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

Does not exist

= Does not exist

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

x \to 4 lim (0)

x \to \infty lim ((\frac{x + 3}{x})^{2 x - 7})

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

x \to 1 lim (\frac{x + 1}{6 x ^{2} + 3 + 3 x})

What is the limit as x approaches 2 of (x-2)^{(x-2)} ?
The limit as x approaches 2 of (x-2)^{(x-2)} is Does not exist