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Review Test

Review Test

Review Test

Review Test

1. Let f (x) = x) for x > 0, and f (x) = 0 for x≤ 0. Which of the following is true?

2. Compute .

3. Let g(x) = 1/x (with domain | x| > 0). Which of the following statements is true of g?

4. The function f (x) = sin(x) is invertible when defined on which of the following domains?

5. What is the value of x sin(1/x)?

6. Let f (x) = ax + b. The inverse function of f (x) has slope

7. Let f (x) = x2 for x≠1 and let f (1) = 2. Then f (x) equals

8. The degree of the product of two degree 3 polynomials is equal to

9. Which of the following points is equal to the image of some real number in the domain of the function f (x) = 2 sin(2x)?

10. The inverse function of f (x) = (1/3)e2x is

11. Find the derivative of sin(ex).

12. Compute the derivative of .

13. Find the derivative of cos(sin(x))).

14. Compute the derivative of 25x2 + 4.

15. What is the derivative of log x?

16. What is the derivative of | x| at x = 0?

17. Find the derivative of e2x+1.

18. Compute the derivative of 1/(x2 + 1).

19. What is the derivative of at x = 1/2?

20. Find the third derivative of f (x) = 2 sin(3x).

21. What is the derivative of tan(x) at x = Π/2?

22. Compute the derivative of f (x) = (x2 +1)log x.

23. Find f'(x), where f (x) = e-x + x.

24. Compute the derivative of x3 + x + 1/x + 1/x3.

25. Find the values of x at all the critical points f (x) = x3/3 - x2 + x.

26. Find the derivative of 1/tan(x).

27. What is the minimum value of ex - x?

28. Find the maximum value of sin(x) + cos(x).

29. Find the minimum value of x2 - 6x + 11 on the interval [2, 5].

30. Find all values of x at which the derivative of f (x) = log| x| - x is zero.

31. Use implicit differentiation to find the slope of the tangent line to the graph of the equation x2y4 = 2x2 + y at the point (1, - 1).

32. Which of the following is an antiderivative of -1/x2?

33. What is the y-intercept of the tangent line to the graph of x2 at x = 3?

34. Find the second derivative of x log x.

35. What is the x-intercept of the tangent line to the graph of ex at x = 0?

36. Compute the maximum vertical distance between the graphs of cos(x) and sin(x).

37. If an ostrich's velocity at time t is given by log(t2), what is the ostrich's acceleration at time t = 4?

38. What are the values of x at inflection points of x3 -3x2 + x + 1?

39. Compute L2(sin(x), - Π, 0).

40. Find L4(sin(x), - Π, 0).

41. Compute 4x3dx.

42. Find cos(x)x.

43. Compute (1/x)dx.

44. Find the upper Riemann sum U48(5, 1, 2).

45. Compute (1 - cos2(x))dx + (- sin2(x))dx.

46. Which of the following is an antiderivative of 4(x + 1)3?

47. Find t2 - 1dt.

48. Compute sin(2x)dx.

49. What is (- 1/x2)dx?

50. The term 'indefinite integral' is equivalent to which of the following terms?