1. BC Content Review

2. When you see… Find the limit of a rational function You think… (If the limit of the top and bottom are BOTH 0 or infinity…)

3. Find the LIMIT

4. When you see… Find You think…

5. Improper Integral! Also use improper integrals when lower bound is infinity OR when there is an undefined value within the bounds.

6. You think… When you see…

7. Logistical Growth P is growing fastest when P = half of carrying capacity M

8. You think… When you see… Find Where factors

9. Think: Partial Fractions!

10. You think… When you see… The position vector of a particle moving in the plane is Find the velocity…

11. Particle Motion Velocity is the derivative of Position

12. You think… When you see… The position vector of a particle moving in the plane is Find the acceleration…

13. Particle Motion Acceleration is the second derivative of Position

14. You think… When you see… The position vector of a particle moving in the plane is Find the SPEED…

15. Particle Motion Speed is the Magnitude of Velocity

16. You think… When you see… Given the velocity vector And position at time 0, find the position vector.

17. Particle Motion Position is the antiderivative of Velocity Integrate x’(t) and y’(t) separately. Use the initial condition of each variable to find the constants of integration.

18. You think… When you see… Given the velocity vector When does the particle stop?

19. Particle Motion Particle stops when the Velocity of the particle is zero

20. You think… When you see… Given the velocity vector Find the slope of the tangent line to the vector v(t) at a given time.

21. Particle Motion

22. You think… When you see… Find the area inside the polar curve

23. Polar Area

24. You think… When you see… Find the slope of the tangent line to the polar curve

25. Polar to Rectangular

26. You think… When you see… Find the horizontal tangents to a polar curve

27. Polar

28. You think… When you see… Find the vertical tangents to a polar curve

29. Polar

30. You think… When you see… Use Euler’s Method to approximate a y-value

31. Euler’s Method (based on local linearity)

32. You think… When you see… Is Euler’s approximation an underestimate or an overestimate?

33. Euler’s Method (based on local linearity) Look at the signs of the derivative and the second derivative in the interval. This gives you the trend and shape of the curve. Sketch a picture to determine the answer.

34. You think… When you see…

35. Integration by Parts

36. You think… When you see… Write a series for where n is an integer

37. Series – (Serious about…) Multiply each term by

38. You think… When you see… Write a series for centered at x=0

39. Series – (Serious about…) Find the Maclaurin polynomial:

40. You think… When you see…

41. Series – (Serious about…) Series converges if p>1

42. You think… When you see… Find the interval of convergence of a series.

43. Series – (Serious about…) Use a test (ratio test) to find the interval of convergence. Then test the convergence of the endpoints.

44. You think… When you see…

45. Series – (Serious about…) Plug in and factor. This will be a geometric series:

46. You think… When you see…

47. Series – (Serious about…)

48. You think… When you see…

49. Series – (Serious about…)

50. You think… When you see…

51. Series – (Serious about…)

52. You think… When you see… Let S 4 be the sum of the first 4 terms of an alternating series f(x). Approximate

53. Series – (Serious about…) This is the error for the 4 th term of an alternating series which is simply the 5 th term (the first neglected term of the series). Always positive since you are looking for an absolute value.

54. You think… When you see… Suppose Write the first four terms and the general term of a series for f(x) centered at x=c.

55. Series – (Serious about…) You are being given a formula for the derivative of f(x)

56. You think… When you see… Given a Taylor series. Find the Lagrange form of the remainder for the nth term where n is an integer at x=c.

57. Series – (Serious about…) You need to determine the largest value of the 5 th derivative of f at some value of z. You are usually given this. Then:

58. You think… When you see… Given f(x), find the arc length on [a,b]

59. Arc Length

60. You think… When you see… Given x=f(t),y=g(t), find the arc length on [t 1,t 2 ]

61. Arc Length

62. You think… When you see… Find Where m and n are integers

63. Trig Integration In order to integrate a powers of sine and cosine, convert functions so that you have either sine or cosine to the first power (for the du). Then change to u and use u-substitutions. Use Pythagorean identities or power reducing formulas.

64. You think… When you see… Given x=f(t),y=g(t), find

65. Parametric - Derivative

66. You think… When you see… Given x=f(t),y=g(t), find

67. Parametric 2 nd Derivative Find the 2 nd derivative by making a rational function with the derivative of the first derivative as the numerator and the original denominator as the denominator.