What is the limit as x approaches 0 of (xsin(1/x))^2 ?

The limit as x approaches 0 of (xsin(1/x))^2 is 0

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limit as x approaches 0 of (xsin(1/x))^2

x \to 0 lim ((x sin (\frac{1}{x}))^{2})

0

Solution steps

x \to 0 lim ((x sin (\frac{1}{x}))^{2})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= (x \to 0 lim (x sin (\frac{1}{x})))^{2}

Apply the Squeeze Theorem:

0

= 0^{2}

Simplify

= 0

x \to \frac{- π}{2} lim (sec (x))

x \to 0 lim (6 (\frac{1}{x} - cot (x)))

x \to \frac{3 π}{4} + lim (2 tan (2 x))

x \to 0 lim ([1 - \frac{∣ x ∣}{x}])

x \to 5 lim (\frac{x + 2}{2 x - 4})

What is the limit as x approaches 0 of (xsin(1/x))^2 ?
The limit as x approaches 0 of (xsin(1/x))^2 is 0