Blank Exam 3-Math 231 -SP 23
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School
University of Illinois, Urbana Champaign *
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Course
231
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
8
Uploaded by DeanFox4079
Math 231 Exam 3. April 10, 2023
Name (printed clearly):
Net ID:
UIN:
TA’s name and discussion section:
Do not open the exam booklet until you are told to begin the exam.
•
Put away everything except a writing utensil. This includes cell phones and electronic
devices (they must be turned off prior to the start of the exam). If you are seen using
these devices during the exam, it will be construed as cheating and you will be asked
to leave. Your book bags should be closed throughout the exam.
•
Academic honesty is required and expected.
•
All books, notes, and other such items must be put away and out of sight.
Please
remove all hats and sunglasses.
•
Calculators are not permitted on this test.
•
Do each of the problems and show
all
work.
•
Partial credit will be given for partially correct work.
•
Box or circle your final answer.
•
If you finish
before 8:10
, you may quietly turn in your exam and leave. You must
show your ID to the proctor at this time. No exam will be accepted without an ID.
•
All students who are still taking the exam at 8:10 must remain seated until the end
of the examination period, which is at 8:20. At that time, everyone will be instructed
to stop working on the exam. Your writing utensil should be put down and the exam
booklet closed. Anyone who does not follow these instructions will earn zero points on
the page they have open. You will then show your ID to the proctor. No exam will be
accepted without an ID.
•
The exam is double-sided and there are 6 questions on the exam.
•
If you have any questions during the exam, please raise your hand and a proctor will
come to you as soon as possible.
Read each question carefully, write your solution clearly, and check your work.
Good luck on the exam!
I certify that I have read, understood, and agree to abide by the above exam directions.
Signature:
1.
(12 points) Determine whether each
sequence
converges or diverges. If it converges,
find the limit. (Recall that lim
x
→
0
sin(
x
)
x
= 1.) You must show work to receive credit.
(a)
a
n
=?
(b)
a
n
=?
(c)
a
n
=?
(d)
a
n
=?
2.
(12 points) Use geometric series or
p
-series to determine whether each series converges
or diverges. You must show work to receive credit.
(a)
∞
X
n
=2
?
(b)
∞
X
n
=1
?
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(c)
∞
X
n
=1
?
(d)
?
?
+
?
?
+
?
?
+
?
?
+
...
3.
(12 points) Use Direct Comparison Test, Limit Comparison Test, Ratio Test, or Root
Test to determine whether each series converges or diverges. You must show work to receive
credit.
(a)
∞
X
n
=1
(
?
?
)
(b)
∞
X
n
=1
?
(c)
∞
X
n
=1
?
(d)
∞
X
n
=1
?
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4.
(6 points) Use the Alternating Series Test to determine whether each series converges
or diverges. You must show work to receive credit.
∞
X
n
=0
?
5.
(6 points) Use the Integral Test to determine whether the series converges or diverges.
You must show work to receive credit.
∞
X
n
=3
?
?
6.
(12 points) Determine whether the given series is absolutely convergent, conditionally
convergent, or divergent. You must show work to receive credit.
(a)
∞
X
n
=1
?
(b)
∞
X
n
=1
?