1. 1.2 Finding Limits Graphically and Numerically

2. Objectives
Study and use a formal definition of a limit.

3. An Informal Definition of a Limit
c - δ c
c + δ
DeltaEpsilonDemo

4. ε-δ Definition of a Limit
Cauchy gave us the standard ε-δ definition of a limit
"f(x) becomes arbitrarily close to L"
The distance between f and L is less than some really, really small value ε.
"as x approaches c."
The distance between x and c is less than some really small value of δ.

5. Formal Definition of a Limit
Let f be a function defined on an open interval containing c (except possibly at c), and let L be a real number. The statement
means that for each ε>0, there exists a δ>0 such that if
You determine how close (accurate) you want L to be to f (and how small ε is) and you find a δ that makes that happen.

6. Example

7. Example

8. Example

9. Homework 1.2 (page 55) #23-29 odd Answers: 23. L=8 25. L=1 27. L=5