1. From sec 2.1 : Find: OUR GOAL Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

2. Example: Find We say that the limit of f(x) as x approaches 2 from the right is equal to 4 The symbol x  2+ means that we consider only values of x > 2 We say that the limit of f(x) as x approaches 2 from the left is equal to 4 The symbol x  2- means that we consider only values of x < 2 Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

3. Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

4. Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

5. Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

6. For the function whose graph is given below Determine the following limits Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

7. Exam-I Term-122 Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

8. Find: 1 Create a table: watch the behavior 2 Use the Graph to find the limit Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

9. Example: Find Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

10. Example: Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

11. - Can we use Direct Substitution Prop.?? Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

12. Can we use Direct Substitution Prop.?? Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

13. Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

14. Find: 1 Create a table: watch the behavior 2 Use the Graph to find the limit 3 Given the function f(x) Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

15. Exam-1 Term 122 1)Common Factors 2)Conjugate radical case Exam-1 Term 121 Example Example: Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

16. 1)Common Factors 2)Conjugate radical case Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

17. What is the difference ?? Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

18. Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

19. Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

20. Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

21. Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

22. Squeeze theorem = Sandwich theorem Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

23. Example: Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

24. Exam1-091 Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

25. Limit from one side does not exist Find an example for a function such that the limit from right does not exist Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

26. Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

27. Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

28. Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

29. Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

30. Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

31. Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS

32. Sec 2.2: Limit of Function and Limit Laws Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS