Evaluate limits from tables

A table of function values near $x=a$ provides numerical evidence for the value $f(x)$ approaches as $x$ approaches $a$, distinguishing this limiting value from $f(a)$, which may differ or be undefined. The reasoning includes comparing values from both sides, identifying one-sided limits, and concluding that a two-sided limit does not exist when the sides approach different values; formal $\varepsilon$-$\delta$ proofs and more advanced infinite-limit analysis are beyond this scope.