1. Warmup

2. Warmup

3. Welcome to Class A quote for today: Homework Answers:
Success is the sum of small efforts, repeated day in and day out. Robert Collier (Inspirational Author)
Homework Answers:
Packet p. 1 & 2—“Pushed Beyond the Limit?”
Answer: “There are no limits in life.”

4. Homework Questions?

5. Day 2 Limits & Continuity

6. Groupwork: “Exploring Continuity”

7. Proving Continuity
In order for a function f(x) to be continuous at a point x=c the following three conditions must be met:
f (c ) must exist
exists, which means

8. Example Problem #1
Is the function continuous at x=2 ?

9. Example Problem #2
Is the function continuous at x=2 ?

10. Limits are useful for exploring continuity
Example:
(We will use the calculator to get the graph!)
TBLSET:
TblStart: 2
∆Tbl: 0.01
The limit of a continuous function at some given value of x will be the function evaluated at that value.

11. Limits are useful for exploring continuity (continued)
What type of discontinuity does the following function have?
TBLSET:
TblStart: 2
∆Tbl: 0.01

12. An IMPORTANT example to explore with the calculator
Tblset:
Tblstart: 0
∆tbl: 0.001
Radian Mode!!!
KNOW THIS!!!