Sullivan Microsite TE SAMPLE

Sullivan AP˙Sullivan˙Chapter01 October 8, 2016 17:4
Section 1.6 • The ε-δ Definition of a Limit 147
To ensure that both inequalities are satisfied, we select δ to be the smaller of the
numbers 1 and ε {
5 , abbreviated as δ = min 1, ε }
. Now,
5
{
whenever |x − 2| 0, we need to find a positive number δ so that whenever 0 < |x −c| 0, then x > c 2 > 0, and 1 x < 2 c . Now
1
∣ x − 1 |x − c|
c ∣ =
c|x|
< 2 1
·|x − c| Substitute
c2 |x| < 2 c .
We can make
1
∣ x − 1 c2
c ∣