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<strong>Sullivan</strong> AP˙<strong>Sullivan</strong>˙Chapter01 October 8, 2016 17:4<br />
<strong>Sullivan</strong><br />
144 Chapter 1 • Limits and Continuity<br />
That is, whenever x = 2 and x differs from 2 by less than 0.1, then f (x) differs from 7<br />
by less than 0.3.<br />
Now, generalizing the question, we ask, for x = 2, how close must x be to 2 to<br />
guarantee that f (x) differs from 7 by less than any given positive number ε? (ε might<br />
be extremely small.) The statement “ f (x) differs from 7 by less than ε” means<br />
−ε < f (x) − 7
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