1. Mathematics

2. Session Functions, Limits and Continuity - 2

3. Session Objectives  Sandwich Theorem  Limits of Trigonometric Functions  Limits of Exponential Functions  Limits of Logarithmic Functions  Limit at Infinity

4. Theorem Note: If f(x)<g(x) for all x, then we can not say that. If f and g are real functions defined in an open interval containing a such that and both exist. Then,

5. Sandwich Theorem Let f, g, h be real functions defined in an open interval containing ‘a’ such that in the neighborhood of ‘a’

6. Limits of Trigonometric Functions

7. Example-1(i) Solution :

8. Example-1(ii) Solution :

9. Example-1(iii) Solution :

10. Solution Cont.

11. Example-1(iv) Solution :

12. Solution Cont.

13. Example-1(v) Solution :

14. Example-1(vi) Solution :

15. Solution Cont.

16. Limits of Exponential Functions

17. Limits of Exponential Functions (Cont.)

18. Limits of Logarithmic Functions

19. Example-2(i) Solution :

20. Solution Cont.

21. Example-2(ii) Solution :

22. Solution Cont.

23. Example-2(iii) Solution :

24. Solution Cont.

25. Example -2 (iv) Solution :

26. Solution Cont.

27. Solution-2 (v) Solution :

28. Solution Cont.

29. Thank you