What is the limit as x approaches 0 of |x|^{sin(x)} ?

The limit as x approaches 0 of |x|^{sin(x)} is Does not exist

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limit as x approaches 0 of |x|^{sin(x)}

x \to 0 lim (∣ x ∣^{s i n (x)})

Does not exist

Solution steps

x \to 0 lim (∣ x ∣^{s i n (x)})

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

then the limit does not exist

x \to 0 + lim (∣ x ∣^{s i n (x)}) = 1

x \to 0 - lim (∣ x ∣^{s i n (x)}) =

Does not exist

= Does not exist

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

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})

What is the limit as x approaches 0 of |x|^{sin(x)} ?
The limit as x approaches 0 of |x|^{sin(x)} is Does not exist