2. © Mark E. Damon - All Rights Reserved Jeopardy Directions for the game: 1. You will need a pencil and paper to keep score. 2. On the next screen, click ONCE on a question. 3. Read the Question and decide on your answer. 4. Click ONCE on the screen If you’re right, add your points to your total. If you are wrong, subtract those points. 5. Click ONCE on the button to go back to try another question. 6. Ready? Click ONCE to go the the Jeopardy board! 7. Press the “Esc” button on the keyboard to end the game. Have fun! Home

3. © Mark E. Damon - All Rights Reserved Derivati ves LimitsIntegrals Applicat ions Misc. Other stuff $100 $200 $300 $400 $500 Final Jeopardy Scores

4. © Mark E. Damon - All Rights Reserved $100 Calculate the derivative of e x Calculate the derivative of e x

5. © Mark E. Damon - All Rights Reserved $100 exex exex Home

6. © Mark E. Damon - All Rights Reserved $200 Calculate the derivative of f(x) = x sin (x) Calculate the derivative of f(x) = x sin (x)

7. © Mark E. Damon - All Rights Reserved $200 f’(x) = x cos (x) + sin (x) Home

8. © Mark E. Damon - All Rights Reserved $300 Calculate the derivative of Y = X 2 (X- 2) 5 Calculate the derivative of Y = X 2 (X- 2) 5

9. © Mark E. Damon - All Rights Reserved $300 Home y’ = 5x 2 (x-2) 4 + (x-2) 5 (2x) y’ = x(x-2) 4 (7x-4) y’ = 5x 2 (x-2) 4 + (x-2) 5 (2x) y’ = x(x-2) 4 (7x-4)

10. © Mark E. Damon - All Rights Reserved $400 Use Implicit Differentiation to calculate y’ X 2 + XY + Y 3 = 3 Use Implicit Differentiation to calculate y’ X 2 + XY + Y 3 = 3

11. © Mark E. Damon - All Rights Reserved $400 2x + xy’ + y + 3y 2 y’ = 0 y’ = -2x – y X + 3y 2 2x + xy’ + y + 3y 2 y’ = 0 y’ = -2x – y X + 3y 2 Home

12. © Mark E. Damon - All Rights Reserved $500 Find the derivative of the following function F(x) = x 3 – 3x 2 + 4 x 2 Find the derivative of the following function F(x) = x 3 – 3x 2 + 4 x 2

13. © Mark E. Damon - All Rights Reserved $500 y’ = x 3 -8 x 3 y’ = x 3 -8 x 3 Home

14. © Mark E. Damon - All Rights Reserved $100 Evaluate Lim 6X - 3 Evaluate Lim 6X - 3 X → 4

15. © Mark E. Damon - All Rights Reserved $100 21 Home

16. © Mark E. Damon - All Rights Reserved $200 Evaluate Lim sin x x Evaluate Lim sin x x X → 0

17. © Mark E. Damon - All Rights Reserved $200 1 1 Home

18. © Mark E. Damon - All Rights Reserved $300 Evaluate Lim l x – 4 l x - 4 Evaluate Lim l x – 4 l x - 4 X → 4

19. © Mark E. Damon - All Rights Reserved $300 No limit Home

20. © Mark E. Damon - All Rights Reserved $400 Evaluate Lim X 2 – 9 X + 3 Evaluate Lim X 2 – 9 X + 3 X → - 3

21. © Mark E. Damon - All Rights Reserved $400 -6 Home

22. © Mark E. Damon - All Rights Reserved

23. $500 Evaluate Lim (X + ΔX) 2 + 1 – (X 2 + 1) ΔX Evaluate Lim (X + ΔX) 2 + 1 – (X 2 + 1) ΔX ΔX → 0

24. © Mark E. Damon - All Rights Reserved $500 (X+ΔX)^2 + 1 – X^1 -1 Δ X cancel 1’s X^2 + 2XΔX + ΔX^2 – X^2 Δ X square and simplify 2X + Δ X Δ X = 0 Answer = 2X. (X+ΔX)^2 + 1 – X^1 -1 Δ X cancel 1’s X^2 + 2XΔX + ΔX^2 – X^2 Δ X square and simplify 2X + Δ X Δ X = 0 Answer = 2X. Home 2X

25. © Mark E. Damon - All Rights Reserved $100 Evaluate ∫ 2x dx Evaluate ∫ 2x dx

26. © Mark E. Damon - All Rights Reserved $100 x 2 + c Home

27. © Mark E. Damon - All Rights Reserved $200 Evaluate ∫ x 3 + 2x x Evaluate ∫ x 3 + 2x x

28. © Mark E. Damon - All Rights Reserved $200 1/3 x 3 +2x + c (cancel one x and then integrate) 1/3 x 3 +2x + c (cancel one x and then integrate) Home

29. © Mark E. Damon - All Rights Reserved $300 Evaluate ∫ (lnx) 3 dx x Evaluate ∫ (lnx) 3 dx x

30. © Mark E. Damon - All Rights Reserved $300 Let U = Lnx, du = 1/x dx = ¼ (ln x) 4 + c Let U = Lnx, du = 1/x dx = ¼ (ln x) 4 + c Home

31. © Mark E. Damon - All Rights Reserved $400 Evaluate ∫ cos 2x dx Evaluate ∫ cos 2x dx

32. © Mark E. Damon - All Rights Reserved $400 ½ sin(2x) + c Home

33. © Mark E. Damon - All Rights Reserved $500 Evaluate ∫xe -x 2 dx Evaluate ∫xe -x 2 dx

34. © Mark E. Damon - All Rights Reserved $500 Let u = -x 2, du = -2x -½ ∫ e u du -½ e -x 2 +c Let u = -x 2, du = -2x -½ ∫ e u du -½ e -x 2 +c Home

35. © Mark E. Damon - All Rights Reserved $100 In an application problem relevant to motion, the first derivative of an equation tells ____________.

36. © Mark E. Damon - All Rights Reserved $100 Velocity Home

37. © Mark E. Damon - All Rights Reserved $200 In an application problem relevant to motion, the second derivative tells ______________.

38. © Mark E. Damon - All Rights Reserved $200 Acceleration Home

39. © Mark E. Damon - All Rights Reserved $300 A hot-air balloon is rising straight up from a level field and is being tracked by a range finder located 500ft from the balloon. At the moment the range finder’s angle of elevation is π/4, the angle is increasing at the rate of 0.14 rad/min. How fast is the balloon rising at that moment?

40. © Mark E. Damon - All Rights Reserved $300 Draw a picture Θ = the angle the range finder makes with the ground Y = the height of the balloon (in feet) T = time, and θ and y are differentiable functions of t. Y = 500 tan θ Y’ = 500 (sec 2 θ)dθ/dt Y’ = 500(2)(.14) = 140ft/min Draw a picture Θ = the angle the range finder makes with the ground Y = the height of the balloon (in feet) T = time, and θ and y are differentiable functions of t. Y = 500 tan θ Y’ = 500 (sec 2 θ)dθ/dt Y’ = 500(2)(.14) = 140ft/min Home

41. © Mark E. Damon - All Rights Reserved $400 Air is being pumped into a spherical balloon to cause its volume to increase at a rate of 100cm 3 /s. How fast is the radius of the balloon increasing when the diameter is 50 cm?

42. © Mark E. Damon - All Rights Reserved $400 1/(25π) cm/s Home

43. © Mark E. Damon - All Rights Reserved $500 Car A is traveling west at 50 mi/h while car B is traveling north at 60 mi/h. Both cars are headed towards intersection C. At what rate are the cars approaching each other when car A is 0.3 mi from the intersection, and car B is 0.4 mi from the intersection?

44. © Mark E. Damon - All Rights Reserved $500 - 78 mi/h Home

45. © Mark E. Damon - All Rights Reserved $100 Find the derivative of y = ln(x 3 + 1) Find the derivative of y = ln(x 3 + 1)

46. © Mark E. Damon - All Rights Reserved $100 y’ = 3x 2 X 3 + 1 y’ = 3x 2 X 3 + 1 Home

47. © Mark E. Damon - All Rights Reserved $200 Find the derivative of y = 6 (x 2 ) Find the derivative of y = 6 (x 2 )

48. © Mark E. Damon - All Rights Reserved $200 y’ = (ln 6)(6^x^2)(2x) Home

49. © Mark E. Damon - All Rights Reserved $300 Find the second derivative of y = x 3 + 3x 2 – ½ x + 5 Find the second derivative of y = x 3 + 3x 2 – ½ x + 5

50. © Mark E. Damon - All Rights Reserved $300 Home y = x 3 + 3x 2 – ½ x + 5 y’ = 3x 2 + 6x – ½ y” = 6x + 6 y = x 3 + 3x 2 – ½ x + 5 y’ = 3x 2 + 6x – ½ y” = 6x + 6

51. © Mark E. Damon - All Rights Reserved $400 Find y’ y = ln [x(1+x) 2 ] Find y’ y = ln [x(1+x) 2 ]

52. © Mark E. Damon - All Rights Reserved $400 y’ = lnx +2ln(1+x) y’ = 1/x +2/(1+x) y’ = lnx +2ln(1+x) y’ = 1/x +2/(1+x) Home

53. © Mark E. Damon - All Rights Reserved $500 A farmer has 2400 feet of fencing to create a rectangular pen for his lamas next to their new barn. If the barn side off the pen does not need a fence, what are the dimensions of the pen with the largest area?

54. © Mark E. Damon - All Rights Reserved $500 A = LW = xy A = 2x + y = 2400 y = 2400 - 2x A = x(2400 – 2x) = 2400x – 2x 2 A’ = 2400 – 4x X = 600 ft Y = 1200 ft A = LW = xy A = 2x + y = 2400 y = 2400 - 2x A = x(2400 – 2x) = 2400x – 2x 2 A’ = 2400 – 4x X = 600 ft Y = 1200 ft Home

55. © Mark E. Damon - All Rights Reserved $100 List the antiderivatives for the following trig functions SinCosTan List the antiderivatives for the following trig functions SinCosTan

56. © Mark E. Damon - All Rights Reserved $100 -cos, sin, sec 2 Home

57. © Mark E. Damon - All Rights Reserved $200 Evaluate the integral ∫ (4 + 3x 2 ) dx Evaluate the integral ∫ (4 + 3x 2 ) dx o 2

58. © Mark E. Damon - All Rights Reserved $200 10 Home

59. © Mark E. Damon - All Rights Reserved $300 When is it good to use implicit differentiation?

60. © Mark E. Damon - All Rights Reserved $300 When an equation can not be easily solved for y in terms of x. Home

61. © Mark E. Damon - All Rights Reserved $400 Complete the statement. Lim [ f(x) + c(g(x))] = Lim f(x) + ________________ Complete the statement. Lim [ f(x) + c(g(x))] = Lim f(x) + ________________ x → a

62. © Mark E. Damon - All Rights Reserved $400 + c Lim g(x) Home x → a

63. © Mark E. Damon - All Rights Reserved $500 In words, state the product rule and the quotient rule.

64. © Mark E. Damon - All Rights Reserved $500 Product rule: first time the derivative of the second + second time the derivative of the first. Quotient rule: bottom time the derivative of the top – top times the derivative of the bottom all divided by the bottom squared. Product rule: first time the derivative of the second + second time the derivative of the first. Quotient rule: bottom time the derivative of the top – top times the derivative of the bottom all divided by the bottom squared. Home

65. © Mark E. Damon - All Rights Reserved Home Calculus Final Jeopardy Question

66. © Mark E. Damon - All Rights Reserved Calculate the derivative of y = 2π 4 Calculate the derivative of y = 2π 4

67. © Mark E. Damon - All Rights Reserved y’ = 0 Home