MTH 287 Study Guide 3

1. / The area of a circle is changing at a rate of At what rate is its radius changing when the radius is 5 in.?
A) B) C) D) E)
2. / Boat dockingSuppose that a boat is being pulled toward a dock by a winch that is 9 ft above the level of the boat deck. If the winch is pulling the cable at a rate of 22 ft/min, at what rate is the boat approaching the dock when it is 12 ft from the dock? Use the figure below.

A) / / D) /
B) / / E) /
C) /
3. / A balloon is being inflated at the rate of 22 cubic centimeters per minute. Find the rate at which the radius is increasing when it is 12 cm (assuming the balloon is a sphere).
A) / 288/11 cm/min / D) / 11/288 cm/min
B) / 24/11 cm/min / E) / 576 cm/min
C) / 11/24 cm/min
4. / Find the differential of
A) / / D) /
B) / / E) /
C) /
5. / The side of a square is measured to be 3 inches with an error of 0.03 in. Find the approximate error and percentage error in the area.
A) / 0.03, 0.33% / D) / 2.0, 1.8%
B) / 0.09, 1% / E) / 0.18, 2%
C) / 0.9, 10%
6. / The edge of a cube is observed to change from 7.0 inches to 7.03 inches. Find the approximate error and percentage error in the surface area.
A) / 25.2, 8.6% / D) / 2.52, 0.86%
B) / 4.41, 1.29% / E) / 2.52, 8.6%
C) / 0.441, 0.129%
7. / The lengths of the edges of a cube are increasing at a rate of 8 ft/min. At what rate is the surface area changing when the edges are 16 ft long?
A) / 384 ft2/min / D) / 6144 ft2/min
B) / 1536 ft2/min / E) / 128 ft2/min
C) / 768 ft2/min
8. / Evaluate the integral .
A) / / D) /
B) / / E) /
C) /
9. / Evaluate the integral .
A) / / D) /
B) / / E) /
C) /
10. / Evaluate the integral .
A) / / D) /
B) / / E) /
C) /
11. / Integrate and simplify.

A) / / D) /
B) / / E) /
C) /
12. / Integrate and simplify.

A) / / D) /
B) / / E) /
C) /
13. / A company has a stock valued at A, in millions of dollars, that changes at a rate given by , where x is the number of years since the year 2000. If the value of the stock is $ million in 2000, find the function that models the total amount of stock company A has.
A) / / D) /
B) / / E) /
C) /
14. / Find the sum of the area of the shaded rectangles under the graph. Round to two decimal places.

A) / 4.25 square units / D) / 5.50 square units
B) / 4.13 square units / E) / 2.75 square units
C) / 4.00 square units
15. / Find the area between the curve and the x-axis from .
A) B) C) D) E)
16. / Evaluate the definite integral .
A) B) C) D) E)
17. / Find for the function f(x) graphed below. The curve shown is a quarter circle.

A) B) C) D) E)
18. / The rate of depreciation of a building is given by dollars per year,Use the definite integral to find the total depreciation over the first years.
A) / / D) /
B) / / E) /
C) /
19. / Evaluate the definite integral .
A) B) C) D) E)
20. / Find the shaded area between the given function and the x-axis.


A) B) C) D) E)
21. / Find the area of the shaded region.

A) B) C) D) E)
22. / Find the area of the shaded region.

A) B) C) D) E)
23. / Equations are given whose graphs enclose a region. Find the area of the region.

A) B) C) D) E)
24. / Equations are given whose graphs enclose a region. Find the area of the region.

A) B) C) D) E)
25. / GENERAL: Design A graphic design consists of a square containing the shape shown below. Find the area of the interior.

A) / square units / D) / square units
B) / square units / E) / square units
C) / square units
26. / Find the area of the shaded region.

A) B) C) D) E)
27. / Evaluate the integral
A) / / D) /
B) / / E) /
C) /
28. / Evaluate the integral
A) / / D) /
B) / / E) /
C) /
29. / Evaluate the integral
A) / / D) /
B) / / E) /
C) /
30. / A new fast-food firm predicts that the number of franchises for its products will grow at the rate , where t is the number of years. If there is one franchise at present , how many franchises are predicted for 63 years from now?
A) B) C) D) E)
31. / If find
A) / / D) /
B) / / E) /
C) /
32. / Find the given integral.

33. / Find the given integral.

34. / Find the given integral.

35. / Find the given integral.

36. / Find the given integral.

ANSWERS

  1. D19. D
  2. A20. B
  3. D21. C
  4. B22. B
  5. E23. A
  6. D24. D
  7. B25. A
  8. A26. B
  9. E27. A
  10. B28. D
  11. D29. A
  12. B30. C
  13. C31. C
  14. B32.
  15. A33.
  16. E34.
  17. E35.
  18. A36.

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