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AP Calculus Semester 2 Final Exam Review & Answers
2. Determine .
3. Compute a left-hand Riemann sum with the intervals indicated
by the table below to approximate the distance traveled.
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t (sec)
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0
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1
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3
|
6
|
10
|
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v (ft/sec)
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15
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21
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28
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36
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45
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4. Find the average value of the function on the interval [1, 5].
5. Find the total area of the region between the x-axis and the graph of in the interval
 .
6. Find the value(s) of x that satisfies the Mean Value Theorem for the function on the interval [1, 11]
7. Find the area between the curves (radian mode).
8. Let R be the region (see graph below) bounded by , the horizontal line y
= 1 and the vertical line
x = 9. Find the volumes generated by revolving the region
about:
(a) the horizontal line y = 1, (b) the x-axis
and (c) the y-axis
9. A solid with a base formed by the region bounded by, the horizontal line y
= 1 and the vertical line x = 9
(see graph below) is formed. For this solid, the cross-sections
perpendicular to the x-axis are
squares. The sides or each square extend from the curve to the horizontal
line y = 1. Find the volume of
the solid.
over
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x
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1
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4
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|
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3
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5
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|
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2
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6
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10. Use the table to the right to determine .
11. Given the velocity of a particle along a coordinate
axis as during the
interval . The
initial position of the
particle is 4. Determine (a) the displacement of the particle, (b) the
total distance the particle traveled and (c) the final position of the
particle
12. =
13.  = 14.  =
15.  = 16.
 =
u = ln x
17. If , determine .
18. Use the Trapezoid Rule to
estimate the distance traveled using the table for the intervals [0, 3] and
[3, 10].
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t (min)
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0
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1
|
3
|
6
|
10
|
|
v (ft/sec)
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15
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21
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28
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36
|
45
|
19. Find the solution for the differential equation with initial
condition for.
Answers:
2.  3. 285 4. –31 5. 3.083 6. x
= 7 8(a). 41.888 8(b). 100.531 8(c). 356.885
9. 13.333 10.
2 11(a). –15 11(b). 17 11(c). –11 12.
13. 14. 15. 16. 17.
18. 320 19.
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