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

2. Homework and Quiz.. WebAssign 1.6 Part II the one problem at the end of your handout is actually classwork, not HW. First quiz tomorrow (1.6 Part I), please prepare for it. Review your HW. Review all the expectations. Points are given to the details, not just the answers.

3. Recall: Limit of a Function

4. Preview Limits with Absolute Values The Squeeze Theorem Pay extra attention to the expectations (especially those who are using your photographic memory!)

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. Expectations Note that solutions steps are very important here. You need to pay attention and understand the acceptable ways of presenting the 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. Expectations

16. Example 9 (Limits with Absolute Values)

18. Squeeze Theorem

19. x y a

20. x y L a

21. x y L a

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

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, 4(c))

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

26. Example 10

28. Expectations

29. Example 10

30. 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 will be ask to state the theorems you learned in this class.