Limits — What Calculus Is Built On

A limit describes what a function approaches as x approaches a value.

Notation: lim(x→a) f(x) = L means as x gets closer to a, f(x) gets closer to L.

Key concept: The limit can exist even if f(a) is undefined. The limit is about APPROACHING, not arriving.

One-sided limits:

lim(x→a⁺) = limit from the right

lim(x→a⁻) = limit from the left

The limit exists only if both one-sided limits are equal.

Limits that don't exist:

Left and right limits differ

Function oscillates infinitely

Function goes to ±infinity (limit is infinite, not a number)

Reference:

Wikipedia: Limit

https://en.wikipedia.org/wiki/Limit_(mathematics)