## Thomas' Calculus 13th Edition

Although $f(x)$ is defined in $[-1,1]$ which means $f(0)$ is defined, it does not mean that the limit of $f(x)$ exists at $x=0$.
For instance, there could be a jump discontinuity at $x=0$, and even though the value there is defined, the limits from the left and right side may not match.