## Thomas' Calculus 13th Edition

(a) For values when $x\in [0, 1)$ (b) For values when $x\in (-1, 0]$
(a) $\lfloor x \rfloor=0$ is true only when $x\geq 0$ and $x<1$ (b) $\lceil x \rceil=0$ is only true when $x>-1$ and $x\leq0$