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

is negative when

x \to 0 -

. Therefore

∣ x ∣ = - x

= x \to 0 - lim ((- x)^{x})

Apply exponent rules

= x \to 0 - lim (e^{x l n (- x)})

Apply the Limit Chain Rule:

1

= 1

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

x \to 0 + lim (sin^{\frac{1}{x}} (x))

x \to 2020 lim (2021)

x \to - 7 - lim (\frac{2 x + 1}{x + 7})

x \to \infty lim (9 x)

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