2. Jeopardy Limits Limits with Trig Slope of a Curve Continuity Potpourri $100 $200 $300 $400 $500 $100 $200 $300 $400 $500

3. $ 100 Click my picture to see the answer Evaluate using any method:

4. Click my picture to return to the Jeopardy Game Board $ 100

5. $ 200 Click my picture to see the answer Evaluate using any method:

6. $ 200 Click my picture to return to the Jeopardy Game Board

7. $ 300 Click my picture to see the answer Evaluate algebraically:

8. $ 300 Click my picture to return to the Jeopardy Game Board -1/2

9. $ 400 Click my picture to see the answer Evaluate algebraically:

10. $ 400 Click my picture to return to the Jeopardy Game Board 3/4

11. $ 500 Click my picture to see the answer Evaluate algebraically:

12. $ 500 Click my picture to return to the Jeopardy Game Board -1/4

13. $ 100 Click my picture to see the answer Evaluate algebraically:

14. $ 100 Click my picture to return to the Jeopardy Game Board

15. $ 200 Click my picture to see the answer Evaluate algebraically:

16. $ 200 Click my picture to return to the Jeopardy Game Board

17. $ 300 Click my picture to see the answer Evaluate algebraically:

18. $ 300 Click my picture to return to the Jeopardy Game Board

19. $ 400 Click my picture to see the answer Evaluate algebraically:

20. $ 400 Click my picture to return to the Jeopardy Game Board 5/2

21. $ 500 Click my picture to see the answer Evaluate algebraically:

22. $ 500 Click my picture to return to the Jeopardy Game Board 2

23. $ 100 Click my picture to see the answer Identify the points of discontinuity and the type

24. $ 100 Click my picture to return to the Jeopardy Game Board X = 0, removable X = 5, non-removable

25. $ 200 Click my picture to see the answer Determine all points of discontinuity.

26. $ 200 Click my picture to return to the Jeopardy Game Board π/3 + 2πn 5π/3 + 2πn

27. $ 300 Click my picture to see the answer Rewrite the following function (if possible) to be continuous for all x. If not possible, explain why.

28. $ 300 Click my picture to return to the Jeopardy Game Board Not possible, x = -2 is a non-removable point of discontinuity

29. Draw a picture of a graph that is not continuous at x = 2 because f(2) does not equal the limit as x approaches 2 of f(x) $ 400 Click my picture to see the answer

30. $ 400 Click my picture to return to the Jeopardy Game Board Draw a graph that has a hole at x = 2 and an extra point above or below the hole.

31. $ 500 Click my picture to see the answer Find the value of k that will make the following function continuous for all x

32. k = 4 $ 500 Click my picture to return to the Jeopardy Game Board

33. $ 100 Click my picture to see the answer Write the equation of the secant line that connects x = -2 and x = 5 on the function f(x) = x 2 in slope-intercept form.

34. $ 100 Click my picture to return to the Jeopardy Game Board

35. $ 200 Click my picture to see the answer If f(x) = 6x 2, find the slope of the curve at x = -3

36. $ 200 Click my picture to return to the Jeopardy Game Board

37. $ 300 Click my picture to see the answer Write the equation of the line that is tangent to f(x) = 5x – 2 at x = 3.

38. $ 300 Click my picture to return to the Jeopardy Game Board

39. $ 400 Click my picture to see the answer Write the equation of the line that is normal to at x = 1

40. $ 400 Click my picture to return to the Jeopardy Game Board

41. $ 500 Click my picture to see the answer Find the point on the function f(x) = x 2 – 6x + 8 where the tangent line is horizontal (if possible).

42. $ 500 Click my picture to return to the Jeopardy Game Board (3, -1)

43. Find the average rate of change of f(x) = x 3 – 3x over the interval [2, 10] $ 100 Click my picture to see the answer

44. $ 100 Click my picture to return to the Jeopardy Game Board

45. Find the equation of the horizontal asymptote for the following function (if possible) using proper limit notation. $ 200 Click my picture to see the answer

46. y = 8 (because the limit as x approaches infinity equals 8) $ 200 Click my picture to return to the Jeopardy Game Board

47. $ 300 Click my picture to see the answer If, what do you know about the graph of f(x)

48. $ 300 Click my picture to return to the Jeopardy Game Board There is a vertical asymptote at x = 4.

49. $ 400 Click my picture to see the answer Find the slope of the curve y = 5x 2 – 3x + 2 at x = a.

50. 10a - 3 $ 400 Click my picture to return to the Jeopardy Game Board

51. $ 500 Click my picture to see the answer At t seconds after lift-off, the height of a rocket is 3t 2 ft. What is the instantaneous rate of change of the height of the rocket at 10 seconds after lift-off?

52. $ 500 Click my picture to return to the Jeopardy Game Board 60 ft/sec