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Q. $\lim\limits_{x \rightarrow \infty} x \, Sin \left( \frac{2}{x} \right) $ is equal to

KCETKCET 2008Limits and Derivatives

Solution:

$\lim\limits_{x\to \infty} \; x \sin \left( \frac{2}{x} \right) = \lim\limits_{\frac{1}{x} \to 0} \frac{\sin \left(\frac{2}{x}\right)}{\frac{1}{2} \left(\frac{2}{x}\right)} = 2 $