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

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

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

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

0

Solution steps

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

Apply the Squeeze Theorem:

0

= 0

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

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