suleimenov (bs26835) – FINAL REVIEW #1 – rusin – (55565)
1
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Here is a review for the final exam.
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posting this in several parts.
001
10.0points
When
f, g, F
and
G
are functions such that
lim
x
→
1
f
(
x
) = 0
,
lim
x
→
1
g
(
x
) = 0
,
lim
x
→
1
F
(
x
) = 2
,
lim
x
→
1
G
(
x
) =
∞
,
which, if any, of
A.
lim
x
→
1
f
(
x
)
g
(
x
)
,
B.
lim
x
→
1
F
(
x
)
g
(
x
)
,
C.
lim
x
→
1
g
(
x
)
G
(
x
)
,
are indeterminate forms?
1.
B and C only
2.
A only
3.
A and B only
4.
B only
5.
all of them
6.
none of them
7.
A and C only
8.
C only
002
10.0points
Determine if
lim
x
→ ∞
x
6
parenleftBig
e
3
/x

1
parenrightBig
exists, and if it does, find its value.
1.
limit = 2
2.
limit =
1
2
3.
limit = 6
4.
limit does not exist
5.
limit = 0
6.
limit = 3
003
10.0points
Determine if the improper integral
I
=
integraldisplay
∞
0
4
(3
x
+ 2)
2
dx
is convergent, and if it is, find its value.
1.
I
= 1
2.
I
=
1
3
3.
I
is not convergent
4.
I
=
2
3
5.
I
=
1
2
6.
I
=
5
6
004
10.0points
Compute the volume of the solid of revolu
tion obtained by rotating the region
R
=
braceleftBig
(
x, y
) :
x
≥
3
,
0
≤
y
≤
4
x
bracerightBig
about the
x
axis.
1.
volume =
25
3
π
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suleimenov (bs26835) – FINAL REVIEW #1 – rusin – (55565)
2
2.
volume =
19
3
π
3.
volume =
28
3
π
4.
volume =
22
3
π
5.
volume =
16
3
π
6.
volume infinite
005
10.0points
Determine if the sequence
{
a
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 Spring '11
 RUSIN
 Limit, Mathematical analysis

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