#### Answer

Yes

#### Work Step by Step

Consider $ |\sin \dfrac{1}{x}| \leq 1, |y \sin \dfrac{1}{x}| \leq y$
$\implies 0 \leq |y \sin \dfrac{1}{x}| \leq |y|$
Since, by the Squeeze Theorem $\lim\limits_{(x,y) \to (0,0) } |y \sin \dfrac{1}{x}| =0 $
and $\lim\limits_{(x,y) \to (0,0) } y \sin (1/x)=0$
Yes, by the Squeeze Theorem the limit for $ \lim\limits_{(x,y) \to (0,0) } y \sin \dfrac{1}{x} =0$ .