1. Section 2.1 INTRODUCTION TO LIMITS

2. Definition of a Limit  Limits allow us to describe how the outputs of a function (usually the y or f(x) values) behave as the inputs (x values) approach a particular value.

3. Limit Notation

4. One and Two Sided Limits  When we say that the function “approaches” a particular value, it can do so moving from the left, or from the right.

5. Another way to think of limits  A function f(x) has a limit as x approaches c if and only if the right-hand and left-hand limits at c exist and are equal. In other words the function must be approaching the same value from both sides.

6. Example

7. Do-Now  Greatest Integer Function (Int x): The function for which…..  Input: all real numbers x.  Output: The largest integer less than or equal to x.  Sketch a graph for this function and complete pg 63 #37-40.

8. Finding limits algebraically

9. Limits of Rational Functions  Can you find the limit as x approaches 3 by using direct substitution?  Why or why not?  Why did the limit not exist in #1 but it did in function #2?  Use algebra to simplify the expressions and confirm the limits that you found graphically.

10. Properties of Limits

11. Properties of Limits Continued

12. Calculator exercise:

13. Examples

14. 142014 – APSI – Day 1 Key Limits that are helpful to know

15. Sandwich Theorem