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
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