serve_file - 2023-12-01T214727.880
pdf
keyboard_arrow_up
School
Rumson Fair Haven Reg H *
*We aren’t endorsed by this school
Course
C101
Subject
Mathematics
Date
Nov 24, 2024
Type
Pages
9
Uploaded by CoachRiverTiger30
February 21, 2023
MA262 - EXAM I
Green Exam: TEST NUMBER
01
Instructions
(1)
DO NOT OPEN THIS EXAM BOOKLET UNTIL TOLD TO DO SO
.
(2) Before you open this exam booklet, fill in the information below and use a #2 pencil to
fill in the required information on your scantron.
(3) On your scantron, write your
10
-digit PUID (starting with “00” from left to right) and
your
4
-digit Recitation section number (starting with “0” from left to right).
(4) This Green exam is TEST NUMBER
01
.
(5) Once you are allowed to open this booklet, check to make sure you have a complete exam.
There are
9
different exam pages including this cover page.
(6) Do any necessary work for each problem in the space provided or on the back of the pages
of this exam booklet. No extra paper is allowed.
Circle
your answers in this exam booklet
in case of a lost scantron.
(7) There are
11
problems, each worth
9
points and everyone gets
1
point.
The maximum
possible score is
100
. No partial credit will be given.
(8) After you finish your exam, hand in both your scantron and your exam booklet to your
instructor, your TA, or one of the proctors.
(9) You may not leave the exam room during the first
20
minutes of the exam.
If you do
not finish your exam within the first
50
minutes, you must wait until the end of the exam
period to leave the room.
Academic Honesty
•
Do not seek or obtain any assistance from anyone to answer questions on this exam.
•
Do not talk during the exam. Any questions should be directed to your instructor or TA.
•
Do not consult notes, books, or calculators during the exam.
Do not handle phones,
cameras, or any other electronic devices until after you have finished your exam, handed
it in to your instructor, your TA or proctor, and left the room.
•
Anyone who violates these instructions will have committed an act of academic dishonesty.
Penalties for academic dishonesty may include an
F
in this course. All cases of academic
dishonesty will be reported immediately to the Office of the Dean of Students.
I have read and understand the above statements regarding academic honesty
:
Student Name
PUID
Student Signature
Recitation Section #
TA Name
1
1.
Find the explicit solution to this initial value problem:
dy
dx
+ 4
xy
3
= 0
,
y
(1) = 1
.
A.
y
=
1
√
2
x
2
-
1
B.
y
=
1
(2
x
2
-
1)
1
3
C.
y
=
1
√
4
x
2
-
3
D.
y
=
x
√
4
x
2
-
3
E.
y
=
1
√
3
x
2
-
2
2.
If
y
(
x
)
is the solution to the initial value problem
xy
′
-
2
y
=
x
3
e
x
y
(1) = 0
,
then
y
(2) =
A.
2
e
2
-
2
e
B.
4
e
2
-
e
C.
2
e
D.
4
e
2
-
4
e
E.
1
2
(
e
2
-
e
)
2
3.
An object initially at
40
◦
F is placed in the air with the air temperature fixed. Suppose
the temperature
T
(
t
)
of the object at time
t
≥
0
satisfies the differential equation
dT
dt
= 2(
T
-
32)
.
What is the temperature (in
◦
F) of the object at time
t
= 1
?
A.
32 + 6
e
B.
32 + 8
e
2
C.
32
D.
40 +
e
2
E.
32 + 8
e
-
2
4.
Find the general solution of the differential equation
dy
dx
= 1 +
(
y
x
)
+
(
y
x
)
2
,
x >
0
.
A.
y
=
x
tan (ln
x
+
C
)
B.
y
=
x
tan (ln
x
) +
Cx
C.
y
=
x
ln (ln
x
+
C
)
D.
y
2
=
x
2
tan (
x
+
C
)
E.
y
2
=
x
3
+
Cx
3
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
5.
A large tank initially contains
40
g of salt in
20
L of water. A solution containing
3
g/L of
salt flows into the tank at a rate of
5
L/min, and the well stirred mixture flows out at the
rate of
2
L/min. Which of the following describes the amount of salt
x
(
t
)
in the tank after
t
minutes?
(g is grams; L is liters)
A.
dx
dt
= 15
-
1
20
x,
x
(0) = 40
B.
dx
dt
= 6
-
2
3
t
x,
x
(0) = 20
C.
dx
dt
= 6
-
1
10
x,
x
(0) = 40
D.
dx
dt
= 15
-
2
20 + 3
t
x,
x
(0) = 40
E.
dx
dt
= 6
-
2
10 + 3
t
x,
x
(0) = 40
6.
Consider the following autonomous differential equation
dx
dt
=
x
2
-
5
x
+ 6
.
Which of one of the following statements is correct?
A.
x
= 2
is an
unstable
critical point and
x
= 3
is a
stable
critical point
B.
x
= 2
is a
stable
critical point and
x
= 3
is an
unstable
critical point
C.
Both
x
= 2
and
x
= 3
are
stable
critical points
D.
x
= 2
is a
stable
critical point and
x
= 3
is a
semistable
critical point
E.
x
= 2
and
x
= 3
are
semistable
4
7.
Find an implicit solution of
(
2
xy
+ 2
xy
2
+ 1
)
+
(
x
2
+ 2
x
2
y
+ 2
y
)
dy
dx
= 0
.
A.
x
2
y
+ 2
x
2
y
2
+
y
2
=
C
B.
x
2
y
+
x
2
y
2
+
x
=
C
C.
x
2
y
+
x
2
y
2
+
x
+
y
2
=
C
D.
2
x
2
y
+
x
2
y
2
+ 2
x
=
C
E.
x
2
y
+
x
2
y
2
+ 2
x
=
C
5
8.
Which of the following three statement(s) is/are TRUE?
(I) The function
y
=
x
2
is a solution to
y
′
= 2
(
y
x
)
.
(II) The differential equation
y
3
y
′
+ 2
x
4
y
4
=
e
x
is a Bernoulli differential equation.
(III) The substitution
v
=
x
+
y
-
1
will transform the equation
y
′
= (
x
+
y
-
1)
2
into a
Separable differential equation.
A.
(I), (II), and (III) are TRUE
B.
Only (II), and (III) are TRUE
C.
Only (I) and (III) are TRUE
D.
Only (I), (II) are TRUE
E.
Only (I) is TRUE
6
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
9.
Consider the linear system
x
1
+ 2
x
2
-
x
3
=
a
3
x
1
-
x
2
+ 3
x
3
= 2
4
x
1
+
x
2
+ 2
x
3
=
b.
Which of the following statement(s) is/are TRUE?
(I) The linear system is consistent for all values of
a
and
b
.
(II) The linear system has infinitely many solutions when
b
=
a
+ 2
.
(III) There is at least one choice of
a
and
b
for which the linear system has exactly one
solution.
A.
Only (I) is TRUE
B.
Only (II) is TRUE
C.
Only (III) is TRUE
D.
Only (I) and (II) are TRUE
E.
Only (II) and (III) are TRUE
7
10.
Consider the linear system
1
0
1
0
2
k
2
1
0
x
y
z
=
1
1
2
.
Find
k
so that the system is inconsistent.
A.
k
= 4
B.
k
=
-
4
C.
k
= 0
D.
k
= 2
E.
No value of
k
8
11.
Find the solutions
x
1
x
2
x
3
of this linear system:
x
1
-
x
2
=
-
2
-
x
1
-
5
x
2
+ 6
x
3
=
2
-
x
1
-
2
x
2
+ 3
x
3
=
2
A.
x
1
x
2
x
3
=
-
2
0
0
B.
x
1
x
2
x
3
=
t
-
1
-
1
0
+
s
-
2
0
0
for all
s, t
∈
R
C.
x
1
x
2
x
3
=
t
1
1
1
+
s
-
2
0
0
for all
s, t
∈
R
D.
x
1
x
2
x
3
=
t
1
1
1
+
-
2
0
0
for all
t
∈
R
E.
x
1
x
2
x
3
=
t
-
1
-
1
0
+
2
0
0
for all
t
∈
R
9
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help