Limits, Informally
Where a function is heading, not where it lands.
Concept
Approach, don't arrive
lim(x→a) f(x) asks what value f(x) closes in on as x gets near a — the value at a itself is irrelevant.
For polynomials and other continuous functions you can just substitute. When substitution gives 0/0, factor and cancel the troublemaker first.
lim(x→a) f(x) = L