1. MAT 3749 Introduction to Analysis Section 2.1 Part 3 Squeeze Theorem and Infinite Limits http://myhome.spu.edu/lauw

2. Notes Group reassignments Math Party Exam 1 Please study for the quizzes

3. Major Themes Introduction to proofs in the context of calculus 1 Make sure future teachers to have a better understanding of calculus 1 Look at (rigorous) ideas in analysis which can be extended to more advanced math

4. References Section 2.1

5. Preview Squeeze Theorem One-sided Limits Limits at Infinities Infinite Limits

6. Squeeze Theorem

7. x y a

8. x y L a

9. x y L a

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

11. Example 1

13. We cannot apply the limit laws since DNE (2.1.1)

14. Example 1 Make sure to quote the name of the Squeeze Theorem.

15. Analysis

16. Proof

17. One-sided Limits

18. Common Notation

19. Consistency…

20. Limits at Infinities

21. It can be shown that (most of the) limits laws remain valid for limits at infinities.

22. Example 2 Use the e-d definition to prove that

23. Analysis Use the e-d definition to prove that

24. Proof Use the e-d definition to prove that

25. Infinite Limits x y a y=f(x) The left-hand limit DNE Notation: is not a number

26. Infinite Limits

27. Example 3 Use the e-d definition to prove that