1. 1.5 LIMITS Calculus 9/16/14

2. WARM-UP

4. LIMITS – P. 49

5. GOAL Find limits graphically or numerically Use properties of limits and analytic techniques to evaluate limits of a function

6. DEFINITION

7. FINDING A LIMIT

8. EX. 1

9. EXAMPLE 2. Graph

10. EXAMPLE 3 Graph

11. EX. 3 Graph

12. FIND THE LIMIT

13. PROPERTIES –P.51

14. OPERATIONS

15. EX 6- FIND THE LIMIT

16. WARM-UP

17. LIMTS Limits are useful when we need to find the value of a function getting close to a certain “x” value We can use direct substitution (“plug in” the x to find the value at that point), but sometimes that is not possible and limits help us see what the function value could be as we approach that x value

18. FIND THE LIMIT

21. ONE- SIDED LIMITS

22. DOES THE LIMIT EXIST OR NOT?

23. FIND A ONE-SIDED LIMIT

24. UNBOUNDED BEHAVIOR

25. COMPARING ONE SIDED LIMITS Ex. 9 in the book.