Answer
$0$
Work Step by Step
We are given the function:
$f(x)=x\sin\dfrac{1}{x}$.
In order to determine $\lim\limits_{x \to 0} f(x)$, we graph $f(x)$ and use zoom and trace features to approximate the limit.
We got:
$\lim\limits_{x \to 0} x\sin\dfrac{1}{x}=0$
