1. Useful Theorems

2. Theorem (1) If has the limit 0, then so is

3. That’ is:

4. Example (1)

5. Theorem (2)

6. Result

7. Example (1) - a

8. Example (1) - b

9. Theorem (4) Let f be a real function & is in the domain of f & The limit of is L f is continues at L Then the limit of is equal to f( L)

10. Examples (1)

11. Solutions

12. Question

13. Theorem (5) The squeeze (Sandwich/pinching) theorem Let, and be sequences such that S n ≤ v n ≤ t n ; n ≥ k where k is any natural number

14. Example (1) - a

16. Solution

17. Example (1) - b

18. Notice that:

19. Solution

20. Example (2)

21. Example (3)

22. Example (4)

23. Theorem(6) ( L' Hospital's rule for sequences ) Let f be a real function and a sequence such that S n = f(n) ; n ε IN. ( that’s is the restriction of f to IN ) The limit at infinity of f is L Then: The limit of the sequence is L

24. Examples (1)

25. Solutions

28. Questions

29. Hints