Limits

This page will include information and problems from "Calculus : Chapter 5 : Limits" By Micheal Spivak

Definition:

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The function $f$ approaches the limit $l$ near $a$ means: for every $\epsilon>0$ there is some $\delta>0$ such that, for all $x$, if $0 < |x - a| < \delta$, then $|f(x) - l| < \epsilon$

With precise notation we have:

(1)

\begin{align} \forall \epsilon \in R^+, \: \exists \delta \in R^+, \: \forall x \in R, \;\; 0<|x-a|<\delta\implies|f(x)-l|< \epsilon \end{align}

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