What kind of discontinuity does the function f(x) = x sin(1/x) have at x = 0 ?
|f(x) = x sin(1/x)|
Since | x sin(1/x) | < | x |, we can see that the limit of f(x) as x approaches zero from either side is zero. Hence, the function has a removable discontinuity at zero. If we set f(0) = 0 then f(x) is continuous.