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# State the formal definition of a limit.

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The formal definition of the limit of a function appears in page 80.

$\text{\underline {Limits of a function }}$ (formal definition)

The limit statement

\begin{aligned} \lim _ { x \rightarrow c } f ( x ) = L \end{aligned}

means that for each number $\epsilon > 0$ there is a number $\delta > 0$ such that

\begin{aligned} \left | f ( x ) - L \right| < \epsilon\quad\text{wherever}\quad 0 < | x - c | < \delta \end{aligned}

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