Compute $\displaystyle{\lim_{x\to0}f(x)}$, where $f$ is defined by
$$ f(x) = \left\{ \begin{array}{ll} x^2 & \quad x \in \Bbb Q \\ x & \quad x \notin \Bbb Q \end{array} \right. $$
I said that the limit is $0$, as plugging $0$ into $x^2$ works and approaching $0$ from the left and the right of $x$ (irrespective of whether $f$ is continuous) works.
