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<strong>Sullivan</strong> AP˙<strong>Sullivan</strong>˙Chapter01 October 8, 2016 17:4<br />
Section 1.6 • The ε-δ Definition of a Limit 145<br />
DEFINITION Limit of a Function<br />
Let f be a function defined everywhere in an open interval containing c, except possibly<br />
at c. Then the limit as x approaches c of f(x) is L, written<br />
lim f (x) = L<br />
x→c<br />
if, given any number ε>0, there is a number δ>0 so that<br />
whenever 0 < |x − c| 0 so that<br />
whenever 0 < |x − (−1)| =|x + 1|
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