Limits and Continuity · Medium problem

A signal's strength near $x=0$ is modeled by $x^2\sin\!\left(\dfrac1x\right)$, where the $\sin(1/x)$ factor oscillates unpredictably and faster and faster as $x\to0$. Does the signal strength settle on a definite value as $x\to0$, and if so, what is it?