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MA  262  Linear Algebra and Differential Equatio...
MA  262  Linear Algebra and Differential Equations  exam MA262 — FINAL EXAM — SPRING 2016 — MAY 2, 2016 TEST NUMBER 01 INSTRUCTIONS: 1. Do not open the exam booklet until you are instructed to do so. 2. Before you open the booklet ﬁll in the information below and use a # 2 pencil to ﬁll in the required information on the scantron. 3. MARK YOUR TEST NUMBER ON YOUR SCANTRON 4. Once you are allowed to open the exam, make sure you h
MA  262  Linear Algebra and Diffe...
MA  262  Linear Algebra and Differential Equations  exam MA262 — FINAL EXAM — SPRING 2016 — MAY 2, 2016 TEST NUMBER 01 INSTRUCTIONS: 1. Do not open the exam booklet until you are instructed to do so. 2. Before you open the booklet ﬁll in the information below and use a # 2 pencil to ﬁll in the required information on the scantron. 3. MARK YOUR TEST NUMBER ON YOUR SCANTRON 4. Once you are allowed to open the exam, make sure you h
Page 1
MA262 — FINAL EXAM — SPRING 2016 — MAY 2, 2016
TEST NUMBER 01
INSTRUCTIONS:
1.
Do not open the exam booklet until you are instructed to do so.
2.
Before you open the booklet ﬁll in the information below and use a # 2 pencil to
ﬁll in the required information on the scantron.
3.
MARK YOUR TEST NUMBER ON YOUR SCANTRON
4. Once you are allowed to open the exam, make sure you have a complete test.
There are 12
diﬀerent test pages (including this cover page).
5. Do any necessary work for each problem on the space provided or on the back of the pages of
this test booklet. Circle your answers in this test booklet.
6. Each problem is worth 10 points. The maximum possible score is 200 points. No partial credit.
7. Use a # 2 pencil to ﬁll in the answers on your scantron
8. After you have ﬁnished the exam, hand in your scantron and your test booklet to your recitation
instructor.
RULES REGARDING ACADEMIC DISHONESTY:
1. Do not leave the exam room during the ﬁrst 20 minutes of the exam.
2. If you do not ﬁnish your exam in the ﬁrst 110 minutes, you must wait until the end of the exam
period to leave the room.
3. Do not seek or obtain any kind of help from anyone to answer questions on this exam. If you
have questions, consult only your instructor.
4. Do not look at the exam of another student. You may not compare answers with anyone else or
consult another student until after you have ﬁnished your exam, handed it in to your instructor
and left the room.
5. Do not consult notes, books, calculators.
6. Do not handle phones or cameras, or any electronic device until after you have ﬁnished your
exam, handed it in to your instructor and left the room.
7. After time is called, the students have to put down all writing instruments and remain in their
seats, while the TAs will collect the scantrons and the exams.
8. Anyone who violates these instructions will have committed an act of academic dishonesty.
Penalties for academic dishonesty can be very severe and may include an F in the 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 dishonesty:
STUDENT NAME:
STUDENT SIGNATURE:
STUDENT ID NUMBER:
SECTION NUMBER
RECITATION INSTRUCTOR:
1
Page 2
1.
Which of the following functions is an integrating factor for the diﬀerential equation
dy
dx
= (ln
x
)
y
+
e
x
?
A.
e
x
ln
x
B.
e
x
ln
x

x
C.
e
x

x
ln
x
D.
e
1
x
E.
x
2.
Consider the diﬀerential equation
dP
dt
=5
(
1

P
4
)
P.
Which of the following statements are true?
I. The equilibrium solutions are
P
= 0 and
P
= 4.
II. The solution
P
(
t
) with
P
(0) = 2 converges to the solution
P
= 4 as
t
→
+
∞
.
III. The solution
P
(
t
) with
P
(0) = 2 converges to the solution
P
= 0 as
t
→
+
∞
.
IV. The solution
P
(
t
) with
P
(0) = 5 converges to the solution
P
= 4 as
t
→
+
∞
.
A. (I) and (IV) only
B. (I) and (II) only
C. (I), (II), and (III) only
D. (I), (II) and (IV) only
E. (II) and (IV) only
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