1. Theorem Interchanging the function & the Limit Sign Let : 1. f be a real function & is in the domain of f 2.The limit of is L 3.f is continues at L Then: The limit of is equal to f( L)

2. Examples (1)

3. Solutions

4. Question

5. Theorem 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

6. Example (1)

7. Example (2)

8. Theorem ( 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

9. Examples (1)

10. Solutions

13. Questions

14. Hints

15. Question 6

16. Hints

17. Question 7

18. Question 8