Bc Review 04 Algebra Worksheet
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5BC Review 04, No calculator (unless specified otherwise)
f
f
1. Let f be a twice differentiable function such that
1
2
and
3
. Which of the following must be
7
true for the function f on the interval 1
?
x
3
5
I. The average rate of change of f is
.
2
9
II. The average value of f is
.
2
5
III. The average value of f is
.
2
(A) None
(B) I only
(C) III only
(D) I and III only
(E) II and III only
dx
2.
x
1
x
3
1
1
x
1
1
x
3
(A)
C
(B)
C
(C)
ln
x
1
x
3
C
ln
ln
x
x
2
4
3
4
1
1
2
x
2
ln
x
1
x
3
C
(D)
ln
C
(E)
2
x
1
x
3
y
x
3. The base of a solid is the region in the first quadrant enclosed by the graphs of
2
and the coordinate
axes. If every cross section of the solid perpendicular to the y-axis is a square, the volume of the solid is
given by
2
2
2
2
2
2
2
2
2
2
2
2
2 y dy
2 y
dy
(A)
(B)
(C)
2 x
dx
(D)
2 x
dx
(E)
2 x
dx
0
0
0
0
0
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