1. 2.1 Rates of Change and Limits Day 1
Calculus AB

2. y = distance in feet t = time in sec
Example 1: A rock breaks loose from the top of a cliff. What is its average speed during the first 2 seconds of the fall? What is its instantaneous speed?
y = distance in feet t = time in sec
Slope of secant line!
t y 2

3. y = distance in feet t = time in sec
y = distance in feet t = time in sec
Instantaneous Speed: slope of the tangent line
(since we don’t have any other point on the tangent, we will use a REALLY close one on the function)
t y 2
2.001

4. Vocab/Formulas
Limit:

5. Does the existence of a limit as xc depend on the existence of f(c)?

6. Theorem 3 Two-Sided Limits
A function f(x) has a limit as x approaches c iff the right-hand and left-hand limits at c exist and are equal.

7. Example 2:

8. Example 3: Using the Theorem about Polynomial and Rational Functions on pg. 62b.

9. Example 3: Using the Theorem about Polynomial and Rational Functions on pg. 62c. d.

10. Example 3: Using the Theorem about Polynomial and Rational Functions on pg. 62e.

11. Pg. 65 Quick Review: 1-9 odd Exercises: 1-20, 39-44
Assignment
Pg. 65 Quick Review: 1-9 odd Exercises: 1-20, 39-44