What is the limit as x approaches 0 of (sin(1/x))^x ?

The limit as x approaches 0 of (sin(1/x))^x is Does not exist

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limit as x approaches 0 of (sin(1/x))^x

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

Does not exist

Solution steps

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

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

then the limit does not exist

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

Does not exist

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

= Does not exist

What is the limit as x approaches 0 of (sin(1/x))^x ?
The limit as x approaches 0 of (sin(1/x))^x is Does not exist