Value of $x^2 \sin (\frac1x)$ at $x=0$ What is the value of $y=x^2 \sin(1/x)$ at $x=0$?  

I see that $x^2 =0$ but $\sin (1/x)$ is undefined.
More generally: if a function made up of a product of functions,  like $y= a(x)b(x)c(x)d(x)\dots$, then at a specific value of $x$ if one of the functions is $0$ and all the other functions are undefined, does it still mean that $y=0$?

If $f(x) = x^2\sin (1/x)$, then $f$ is undefined at $x = 0$, but $\lim_{x\to 0} f(x) = 0$.
