1. MATH 123 MIDTERM 1 TUTORIAL Surath Gomis Saskatoon Engineering Students’ Society surath.gomis@usask.ca October 7, 2015

3. OVERVIEW Preliminaries Limits Continuity Tangents Differentiation

4. PRELIMINARIES

5. EXAMPLE 1

6. EXAMPLE 2

7. LIMITS Limits define the behaviour at boundaries. This behaviour can be different depending on what side you approach from.

8. EXAMPLE 3

9. EXAMPLE 4

10. EXAMPLE 5

11. EXAMPLE 6

12. EXAMPLE 7

13. EXAMPLE 8

14. EXAMPLE 9

15. CONTINUITY Yet more ways to observe the behaviour of functions. Continuity is just as it sounds – a function which traverses without breaks or tears in smoothness is continuous.

16. EXAMPLE 10

17. EXAMPLE 11

18. TANGENTS

19. EXAMPLE 12

20. EXAMPLE 13

21. EXAMPLE 14

22. EXAMPLE 15

23. DIFFERENTIATION

24. EXAMPLE 16

25. GOOD LUCK