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Review of Calculus BC I

Review Test

Table of Contents

Further Reading

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) = x 2 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)e 2x is

11. Find the derivative of sin(e x) .

12. Compute the derivative of .

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

14. Compute the derivative of 25x 2 + 4 .

15. What is the derivative of log x ?

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

17. Find the derivative of e 2x+1 .

18. Compute the derivative of 1/(x 2 + 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) = (x 2 +1)log x .

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

24. Compute the derivative of x 3 + x + 1/x + 1/x 3 .

25. Find the values of x at all the critical points f (x) = x 3/3 - x 2 + x .

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

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

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

29. Find the minimum value of x 2 - 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 x 2 y 4 = 2x 2 + y at the point (1, - 1) .

32. Which of the following is an antiderivative of -1/x 2 ?

33. What is the y -intercept of the tangent line to the graph of x 2 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 e x 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(t 2) , what is the ostrich's acceleration at time t = 4 ?

38. What are the values of x at inflection points of x 3 -3x 2 + x + 1 ?

39. Compute L 2(sin(x), - Π, 0) .

40. Find L 4(sin(x), - Π, 0) .

41. Compute 4x 3 dx .

42. Find cos(x)x .

43. Compute (1/x)dx .

44. Find the upper Riemann sum U 48(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 t 2 - 1dt .

48. Compute sin(2x)dx .

49. What is (- 1/x 2)dx ?

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