1. MAT 1234 Calculus I Section 1.6 Part II Using the Limit Laws http://myhome.spu.edu/lauw

2. Homework WebAssign 1.6 Part II Turn in the one problem at the end of your handout tomorrow. Friday special again this Friday ->OMH 215

3. Recall: Limit of a Function if and only if and Independent of f(a)

4. Preview Limits with Absolute Values The Squeeze Theorem Pay extra attention to the presentation expectations.

5. Recall (absolute value function)

6. Example 8(a) (Limits with Absolute Values) This is not a polynomial or an rational function Absolute function is not in one of the 11 limit laws Find the limit by using the definition of limits

7. Example 8(a) (Limits with Absolute Values) This is not a polynomial or an rational function Absolute function is not in one of the 11 limit laws Find the limit by using the definition of limits

8. Example 8(a) (Limits with Absolute Values) This is not a polynomial or an rational function Absolute function is not in one of the 11 limit laws Find the limit by using the definition of limits

9. Example 8(a) (Limits with Absolute Values) This is not a polynomial or an rational function Absolute function is not in one of the 11 limit laws Find the limit by using the definition of limits

10. Example 8(a) (Limits with Absolute Values) We are going to look at left and right hand limits: 1. 2.

11. Example 8(a) (Limits with Absolute Values) Note that solutions steps are very important here. You need to pay attention and understand the correct way of presenting your solutions. WebAssign do not check your solutions steps. Advise: Write out full solutions in your notebook even WebAssign does not ask for it.

12. Example 8(b)

13. Again, no direct substitution!!

14. 1. 2. Example 8(b)

15. Example 9 (Limits with Absolute Values)

17. Squeeze Theorem

18. x y a

19. x y L a

20. x y L a

21. You will see this type of idea over and over again. x y L a

22. Example 10 We cannot apply the limit laws since DNE (Lab 2, 4(c))

23. Example 10 We cannot apply the limit laws since DNE (Lab 2, 4(c))

24. Example 10 We cannot apply the limit laws since DNE (Lab 2)

25. Example 10

27. Expectations

28. Example 10

29. Review: We learned… How to find limits involving absolute values. The idea of the squeeze theorem. Pay attention to the expectations of the solutions details. Note that in the exam, you may be ask to state the theorems you learned in this class.

30. Quiz Please use pencils and erasers. If your handwriting is difficult to understand,… You have 20 min. Do not look at your neighbor’s paper. If you need to relax your neck, … Double check your work. Once you turn in your paper, you can go.

31. Quiz