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 ∣})

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

then

x \to a lim f (x) = L

x \to 0 - lim (∣ x ∣^{∣ x ∣}) = 1

x \to 0 + lim (∣ x ∣^{∣ x ∣}) = 1

= 1

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