Introduction to Limits · Superchallenge problem

Evaluate $\displaystyle\lim_{x\to2}\big(\lfloor x\rfloor+\lfloor -x\rfloor\big)$, where $\lfloor\,\cdot\,\rfloor$ is the greatest-integer function. Compare the limit to the value of the function at $x=2$, and classify the discontinuity there.