Final Exam
(Mock Test)
Math 12010-003
Answer the cluestions in the spaces provided. Show all of your work.
Name:
ID: U
0
Question:
1
2
3
4
5
6
7
8
9
10
11
Total
Points:
10
10
10
10
10
10
10
5
10
10
5
100
Score:
1. For each of the following problems sketch the region R, shade it and calculate the area.
(a)
5 points Region bounded by y =
y = 0 ..‘r = —8 aind r = 8.
(b) [points Region bounded by x
I
i
C
/
=
4/ arid
x
=
8
— 4y
.
1
‘!
(
1
.L
2.
rfüi)oilIts
Find the voliune of the solid generated by revolving the region R bounded
h y
=
0,
:i:
=
2
4, about the
uid 2
:r-axis.
(Sketch tlw region first and shade
it).
j
2
3.
10 points Find the volume of the solid generated by revolvuig the region R hounded
by y 6i afl(l II = 612, about the .x-axis. (Sketch the region first and shade it).
€
cy
( )k -\) -
L\J
r.(
i)
(2
-
—
—
k.
/
,y
\C)(
—)--
u
.—
-
Page 2
4. 10 points Find the volume of the solid generated by revolving the region R in the first
quadrant bounded by y = x
, y = 2 2 and x = 0, about the y-axis. (Sketch the region
2
first and shade it).
2
c
-
-
(\
D
5.
(a)
1 points
-
Find the length of the arc y
=
(x2
+
1)3/2
between x
=
1 and x
=
-
-
Pc’cc-
&.
-
2.
‘
‘
.rp
-
(:/li
—
THO(I
(i)
( ‘ii)5
•D
\-
f\
r
-
(±x)usx
/
s4lltod
SJThIO4uT otTTJp1iT TiTO1JOJ
ç
()
T-’1”J 9
-‘(
Q\\\
v
1
(J
-
-
--
1
M
c
()
-llxI—d )TJ4
TTiAIOA).T
?
1
J11)([
‘I
>
>
o
=
(ri)
XITTO(T
1)
l).))1?.1)1T) ))lJ.1l
7. Evaluate the following definite integrals.
(a) 5 points
J
(cos 2x + sin 2x) dx
0
k2
2U2—
-3c()
—
r
•j2L
-
-
-
-
(b) 5pointsj
-
3)
2—
L3-
2-
8.
(a) 3 points Evaluate [f(x)dx where f(x)
=
{x
4—x
ifO<x<1
if 1 <x <2
if2<x4
—
2.
Page5
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---
1
-
-
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—C
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fl
—
-
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-
0
-
-
-
II
II
-
II
—
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C)
x
J
-
LI
I
Izi
ii
I
—
o
•
f_S
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N
—
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4
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4—-
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3
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-
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ft \
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U
10. 5 points Sketch the graph of the ftmction y
erties:
(a) Domain of
f
is R
—
=
f(x)
which satisfies the following prop
{—1, 1}.
(b) f(0) = 0, f is concave up on (—1, 0) and (1, +oc), and concave dowil on (—cc, —1)
and (0,1).
(c) There are 2 vertical asymptotes at x
urn
f(x)
=
+oc, lirn
f(x)
=
=
f(x)
=
2 and
—cc and urn
2 and y
=
—2 such that
lim
X-#—DC
f(s)
H
1
Page
7
1 such that
=
x—*1
=
=
f(x)
—cc, urn
(d) There are 2 horizontal asymptotes at y
lim
—1 and x
=
—2.
f(x)
+cc.
I
5H
2
L.
—j
—
V
—,
)—
IA
-
+
C
C
C
A
.,
j_
i
/-
G
1)
*
—
i
I,
CD
CD
Ij
C
Cii
(r,
>-
—LJ
\2-
-
N
Cc
c/ z
+
JD
C
E
C
c—i
DC
—
Li
.1
—
—
CL
0
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J_:H
.%
-N
C.9
+1
ND
0