Name:
Instructor:
Math 20550, Exam 1
February 17, 2015
The Honor Code is in effect for this examination. All work is to be your own.
No calculators.
The exam lasts for 1 hour and 15 minutes.
Be sure that your name is on every page in case pages become det
Multiple Choice
1.(6 pts) If the scalar projection of b onto a is Comp a b = 1, what is Comp 2a 3b?
(a)
2
(b)
5
(c)
3
2
(d)
6
(e)
3
2.(6 pts) Which of the following expressions gives the length of the curve defined by
r(t) = ln(t)i tj + t2 k between the p
B

w!
/
y >
t 1
p
u
r ot c A
T

x
e
P
W
z

LU 
d bcj
"
1
Bk
Q
C
.

.
Z
c

E l
z
, Z 8
,
B
r
h
Scanned by CamScanner
cfw_s 7
,

w
g
p
& 9Q
z
n
im
p
g
(
Scanned by CamScanner
Scanned by CamScanner
h 1J
9
cfw_

m a
L = <
w
+
9
J
Po Y
^
w

n
)
ve
m
E
u u
W;
x o n
Qh a n mm
v
Scanned by CamScanner
Scanned by CamScanner
e

@
.
w
A
A
w
6 u ? l
_
1
A
.

x

Z
e*
e
*
w
0
o tf
v
)
Scanned by CamScanner
, d

Q
1(v )

be
,
m
m
4
F

2
u p :
p
Cu 1 j
L
L
Ie
J

e

)
U<
=
)

v
)
q
9k
]j
V
R
,

C e;
&$
M
(U t e JA
w
R

, J
IH
m

Scanned by CamScanner
Scanned by CamScanner
7F

C w
( Z 3
( w
< l
c

,
_
=
(
.
t
Z a :>
r
.

,
>
<t t
,
>
/
x

(
? ^
L la l
Scanne
Scanned by CamScanner

_
=
.
L g
V
t u , F
Scanned by CamScanner
/
1 w x WWP
.
A :w
F
4G
^
L
n l
m

m
w
ei
m
ME
Scanned by CamScanner
^
=
L.
_
t
u
y

e
* *
m
w

p
t
/
F
l
w
I
!l H
(
3 >y
Vt
J 4
m
e
d
;
:
h ) 52
4
x
z
m
Q
t 9W
W l
I
=
.
h
k
c
@
w

)

Q
d
~
.
Scanned by CamScanner
Scanned by CamScanner
.
.
.
JC
l

.
v
1/ r
t aBr r d
H
yet < u
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
H
2
l
:
h
w
b<#
ie

B? L ;
a
^
M J

(
.

.
.
w
Q
:
)
k
.

.
C
_
.
.
J

2 &
Scanned by CamScanner
c
t
Scanned by CamScanner
c ce
=
_
1T f t l
N
b
.
.
[
rm
2.J 7
e
k
li
I T

d
f
J
m
=
l
t Z LC )
II
m
a
Scanned by CamScanner
Iw
"
n 1 h
n
o
_
v
Scanned by CamScanner
Scanned by CamScanner
Wc h f
vo
v
1m
i
.
i m8
C
Aj
z
M
.
Ws
z
c
t;
.
\
=
()
Scanned by CamScanner
)
t
"
E
i
gggggee 1111
ee
e
<
!
0
3
,
< . m
Zdu e
Q
e
t
o
y
< 4 <4<9.
<4<9;
9 .
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
>
+

w
6
:
.
=
r
CW T

"
^
W

i
e
q
e) J
v

u m tl
.
_
z
A
"
"
Q L
,
"
&:

4

C4
Scanned by CamScanner
Scanned by CamScanner
lf
(
< 
T O
,
_
!
L
cfw_
m
,
>
t
=
L
1
t
?&
)
A
=
Scanned by CamScanner
Multiple Choice
1.(6 pts) Let a = h1, 2, 0 i, b = h3, 1, 1i, and let c = proja b be the vector projection of
b onto a. Which one of the following vectors is orthogonal to b c?
(a)
h0, 1, 1i
(b)
h2, 1, 1i
(d)
h2, 1, 0i
(e)
h1, 0, 1i
(c)
h1, 2, 0i
2.(6 pts)
Name:
Instructor:
Math 20550, Exam 1, Practice
September 22, 2015
The Honor Code is in effect for this examination. All work is to be your own.
No calculators.
The exam lasts for 1 hour and 15 minutes.
Be sure that your name is on every page in case pages
Multiple Choice
1.(6 pts) Find the absolute maximum and minimum of f (x, y) = 4y + x2 2x + 1 on the
closed triangular region with vertices (0, 0), (2, 0) and (0, 2).
(a)
maximum value = 9, minimum value = 0
(b)
maximum value = 10, minimum value = 1
(c)
ma
Name:
Instructor:
Math 20550, Exam 2
March 17, 2015
The Honor Code is in effect for this examination. All work is to be your own.
No calculators.
The exam lasts for 1 hour and 15 minutes.
Be sure that your name is on every page in case pages become detach
ZZZ
(x2 + y 2 ) dV , where
Problem 1. Use cylindrical coordinates to evaluate
E
p
E = cfw_(x, y, z)  x2 + y 2 z 2.
Solution. In cylindrical coordinates the region is 0 2, r 2 and r z 2. The
integral is
Z 2 Z 2
Z 2
ZZZ
Z 2 Z 2 Z 2
8
16
3
3
2
2
r dzdrd =
r
Multiple Choice
1.(6 pts) Let f (x, y) be a function where (1, 3) and (1, 0) are critical points. We also
know that fxx (1, 3) = 1, fx,y (1, 3) = 2, fyy (1, 3) = 1 and fxx (1, 0) = 2, fx,y (1, 0) =
1, fyy (1, 0) = 3. Using the second derivative test class
Name:
Instructor:
Math 20550, Practice Exam 2
September 30, 2015
The Honor Code is in effect for this examination. All work is to be your own.
No calculators.
The exam lasts for 1 hour and 15 minutes.
Be sure that your name is on every page in case pages
Name:
Instructor:
Math 20550. Exam 3, Practice Exam
November 7, 2015
The Honor Code is in effect for this examination. All work is to be your own.
No calculators.
The exam lasts for 1 hour and 15 minutes.
Be sure that your name is on every page in case pa
l s
A w
^
)

r
.
"
.

p g a
x
/
t
/
2
& r( .
^
Cm
C
A

B
)
1 D
8

,
<
oJ
:
2
m
Scanned by CamScanner
Z
z
z
`
x
A
t
.

lt
j
e
2
e
z
+
2
A

h
)
Q
z
y
e
A
z
)A Z z Z

x
l
A 5
2
l
1
z
0
z
z
.
r
o
A
1 =
z 0

o
m

:
w
w
,
?
,
Scanned by CamScanner
cr
J l;


e
1
t lu
f
ra tu
: :
h a l
Scanned by CamScanner
,
zI
L
L
e
M
p
w

)
2

? 2


r )B
"

x\
c l c
Scanned by CamScanner
Scanned by CamScanner
J
w
2
/
y
:
)
c MU
r lb

4/
4e j 7
Q
,
e