# Limits – Calculus Section 1.1

Definition of a Limit

Let $f(x)$ be defined for all $x$ in an interval about $x = a$ but not necessarily at $x = a$. If there is a number $L$ such that to each positive number $\epsilon$ there corresponds a positive number $\delta$ such that

$|f(x) - L| < \epsilon$ provided  $0 < |x - a| < \delta$,

we say that $L$ is the limit of $f(x)$ as $s$ approaches $a$, and write

$\lim \limits_{x \to a} f(x) = L$

Quick Calculus by Daniel Kleppner and Norman Ramsey – 2nd Edition, 1985