Math 119

Practice Final Exam

This practice exam will not contain samples of all of the problems types studied during the semester. It may not parallel the actual final exam very closely. It is intended for general review purposes. Students should not limit their review efforts to this document.

1. Find the derivative of .

2. Integrate:

3. For the probability density function, , find the mean.

4. Find the definite integral:

5. Describe the relative extrema of

6. Find the sum of 20+10+5+5/2+…

7. Find the average rate of change of the function between x = 1

and x = 2.

8. Integrate:

9. Find the equation of the tangent line to when x = 1.

10. Evaluate the definite integral:

11. Find the Taylor Polynomial of degree 4 at 0 for .

12. Find the derivative of .

13. Find the indefinite integral: .

14. If , find

15. The function has a saddle point. Find

the values of x and y which will indicate its location.

16. An object is moving in such a way that its distance from the starting point is

given by . Find expressions for its velocity and

acceleration.

17. Find the maximum value of

18. Solve for y if y = 0 when x = 1.

19. Find the vertex of the parabola

20. Find the volume of the solid of revolution bounded by

21. Find the derivative of .

22. Find the area between the curves:

23. Find the intervals where the function is concave up and where it is concave

down.

24. Find the limit:

25. Find

26. If , solve for y

27. Calculate this double integral:

28. Find the intervals where the function is increasing and/or decreasing:

29. Find the derivative of

30. Given for x , find the mean and the standard deviation.

31. Find the equation of the tangent line to the curve at the point (16,2).

32. Integrate:

33. The city park department is planning an enclosed play area in a new park. One side of the area will be against an existing building, with no fence needed there. Find the dimensions of the maximum rectangular area that can be mad with 900 m of fence.

34. Evaluate:

35. Find the derivative of

36. Find the equation of the tangent line to the curve at the given value of x.

x = 3

37. Determine the intervals over which the function is increasing or decreasing:

38. A company plans to package its product in a cylinder that is open at one end.

The cylinder is to have a volume of . What radius should the circular

bottom of the cylinder have to minimize the cost of material?

39. Find the integral:

40. Evaluate the definite integral:

41. Find the area between the curve and the x-axis over the indicated closed

interval:

42. Find the area enclosed by the group of curves:

43. Evaluate the definite integral:

44. Find the volume of the solid of revolution formed by rotating the bounded

region about the x-axis.

45. Evaluate the double integral:

46. Find the second order partial derivative :

47. Suppose you were offered a job in which you would be paid one cent on the first day, 2 cents on the second day, 4 cents on the third day, 8 cents on the fourth day and so on for thirty days. How much money would you earn in 30 days?

48. Find the indefinite integral:

49. A company wants to provide for future expansion by making continuous deposits to an account, with no initial deposit. The money will earn interest at a

rate of 10% compounded continuously. If the company needs to accumulate $500,000 in 3 years, how much will the annual deposit need to be?

50. A probability density function is defined by for x in [0.1].

Find the expected value, the variance and the standard deviation.

Answers:

1.

2.

3. 1.5

4.

5. Relative minimum at (15, -8)

6. 40

7. 1

8. 1

9. y = -31x +24

10. -1/3

11.

12.

13.

14. 54

15. (10, -3)

16.

17. 528

18.

19. (-4, -11)

20.

21.

22. 4/3

23. Concave up Concave down

24. 7

25.

26. y = Mx

27.

28.

29.

30. both are 90.

31.

32.

33. 225m by 450 m

34. 2/5

35.

36.

37. Decreasing on , increasing on

38. 3 inches

39.

40.

41.

42.

43.

44.

45. e – 1

46.

47. $10,737,418.23

48.

49.

50. expected value (mean) .5833; variance standard deviation