1. Chapter 2 Review Calculus

2. Quick Review 1.) f(2) = 0 2.) f(2) = 11/12 3.) f(2) = 0 4.) f(2) = 1/3

3. Slide 2- 3 Quick Review (-4, 4) (-1, 5)

4. Slide 2- 4 Example Limits Remember to always try to plug in what you are approaching, if you get a value then that is your limit.

5. Slide 2- 5 Example Limits

6. [-6,6] by [-10,10] by graphing:

7. Slide 2- 7 Example One-Sided and Two-Sided Limits o 12 3 4 Find the following limits from the given graph.

8. Slide 2- 8 Quick Review Solutions [-12,12] by [-8,8][-6,6] by [-4,4]

9. Slide 2- 9 Quick Review Solutions

10. Slide 2- 10 [-6,6] by [-5,5] Example Horizontal Asymptote

11. Slide 2- 11 Example Sandwich Theorem Revisited

12. Example Vertical Asymptote [-6,6] by [-6,6]

13. Example “Seeing” Limits as x→±∞

14. Slide 2- 14 Quick Quiz Sections 2.1 and 2.2

15. Slide 2- 15 Quick Quiz Sections 2.1 and 2.2

16. Slide 2- 16 Quick Quiz Sections 2.1 and 2.2

17. Slide 2- 17 Quick Review Solutions

18. Slide 2- 18 Quick Review Solutions

19. Slide 2- 19 Quick Review Solutions

20. Slide 2- 20 Quick Review Solutions

21. Slide 2- 21 Example Continuity at a Point o

22. Slide 2- 22 Continuity at a Point x = 0 Continuous Removable DiscontinuityRemovable Jump Dis. Infinite Dis. Oscillating functions are not continuous, infinite discontinuity

23. Example Continuity at a Point [-5,5] by [-5,10]

24. Slide 2- 24 Continuous Functions [-5,5] by [-5,10]

25. Quick Review Solutions

26. Slide 2- 26 Quick Review Solutions

27. Slide 2- 27 Quick Review Solutions

28. Slide 2- 28 Average Rates of Change The average rate of change of a quantity over a period of time is the amount of change divided by the time it takes. In general, the average rate of change of a function over an interval is the amount of change divided by the length of the interval. Also, the average rate of change can be thought of as the slope of a secant line to a curve.

29. Slide 2- 29 Example Average Rates of Change

30. Example Tangent to a Curve

32. Slide 2- 32 Slope of a Curve

33. Slide 2- 33 Slope of a Curve at a Point

34. Slide 2- 34 Normal to a Curve The normal line to a curve at a point is the line perpendicular to the tangent at the point. The slope of the normal line is the negative reciprocal of the slope of the tangent line.

35. Slide 2- 35 Example Normal to a Curve

36. Slide 2- 36 Quick Quiz Sections 2.3 and 2.4

37. Slide 2- 37 Quick Quiz Sections 2.3 and 2.4

38. Slide 2- 38 Quick Quiz Sections 2.3 and 2.4

39. Chapter Test Solutions

40. Slide 2- 40 Chapter Test Solutions

42. Slide 2- 42 Chapter Test

43. Slide 2- 43 Chapter Test Solutions

44. Slide 2- 44 Chapter Test Solutions