Estimating a limit at a point discontinuity from a table of values

Looking at the table, as $x$ approaches $2$ from the left (values $1.9, 1.99, 1.999$), $f(x)$ approaches $7$ from below ($6.7, 6.97, 6.997$). As $x$ approaches $2$ from the right (values $2.1, 2.01, 2.001$), $f(x)$ also approaches $7$, this time from above ($7.3, 7.03, 7.003$). Since both one-sided trends converge to the same number, the two-sided limit exists and equals $7$.

The actual value $f(2) = 10$ is irrelevant to the limit computation, since the limit depends only on values of $f$ near $2$, not at $2$. Therefore $\lim_{x\to 2} f(x) = 7$, while $f(2) = 10$, so the limit does not equal the function value at that point — this reflects a removable (point) discontinuity.