Sullivan Microsite DigiSample
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
<strong>Sullivan</strong> AP˙<strong>Sullivan</strong>˙Chapter01 October 8, 2016 17:4<br />
<strong>Sullivan</strong><br />
146 Chapter 1 • Limits and Continuity<br />
EXAMPLE 2<br />
Using the ε-δ Definition of a Limit<br />
Use the ε-δ definition of a limit to prove that:<br />
(a) lim<br />
x→c<br />
A = A, where A and c are real numbers<br />
(b) lim<br />
x→c<br />
x = c, where c is a real number<br />
Solution (a) f (x) = A is the constant function whose graph is a horizontal line. Given<br />
any ε>0, we must find δ>0 so that whenever 0 < |x − c| < δ, then | f (x) − A|
Change language