1. Lesson 2-1: Rates of change and Limits Day #2
AP Calculus
Mrs. Mongold

2. One-sided and Two-sided Limits
When the values of a function f tend to be different limits as x approaches a number c from opposite sides we call the limit a two-sided limit.
When x approaches c from the right it is called a right hand limit
When x approaches c from the left it is called a left hand limit
Right Hand: Left Hand:

3. Theorem
A function f(x) has a limit as x approaches c if and only if the RHL and LHL at c are equal

4. Example 1

5. Example 2

6. Example 3
Find the limit at
x=0
x=1
x=2
x=3
x=4

7. Greatest integer function

8. Sandwich Theorem (a.k.a. Squeeze Theorem)
Use this when the limit cannot be found directly
If g(x) < f(x) < h(x) for all x≠c in some interval about x, and

9. Example

10. Example

11. Homework
Pg 62-63/ 1-6 all and 31 and 32