MATH-1080 Midterm: 201708_Test_3A
31 Jan 2019
School
Department
Course
Professor
MATH 1080
Calculus of One Variable II
Test 3
Version A
Fall 2017
Sections 11.5 - 11.11,
Appendix C, 10.1, 10.2
Student’s Printed Name: CUID:
Instructor: Section:
Instructions: You are not permitted to use a calculator on any portion of this test. You are not
allowed to use any textbook, notes, cell phone, laptop, tablet, SMART watch, or any technology
on any portion of this test. All devices must be turned off while you are in the testing room.
During this test, any communication with any person (other than the instructor or a designated
proctor) in any form, including written, signed, verbal, or digital, is understood to be a violation
of academic integrity.
No part of this test may be removed from the examination room.
Read each question carefully. In order to receive full credit for the free response portion of the test,
you must:
1. Show legible and logical (relevant) justification that supports your final answer.
2. Use complete and correct mathematical notation.
3. Include proper units, if necessary.
4. Give exact numerical values whenever possible.
You have 90 minutes to complete the entire test.
On my honor, I have neither given nor received inappropriate or unauthorized infor-
mation at any time before or during this test.
Student’s Signature:
Do not write below this line.
Free Response Possible Points Free Response Possible Points
Problem Points Earned Problem Points Earned
1. 12 4(b). 5
2(a). 7 4(c). 5
2(b). 7 5. 12
3(a). 10 Free Response 70
3(b). 7 Multiple Choice 30
4(a). 5 Test Total 100
Version A - Page 1 of 12
MATH 1080
Calculus of One Variable II
Test 3
Version A
Fall 2017
Sections 11.5 - 11.11,
Appendix C, 10.1, 10.2
Multiple Choice: There are 10 multiple choice questions. They all have the same
point value. Each question has one correct answer. The multiple choice problems will
count for 30% of the total grade. Use a number 2 pencil and bubble in the letter of
your response on the scantron sheet for problems 1 - 10. For your own record, also
circle your choice on your test since the scantron will not be returned to you. Only
the responses recorded on your scantron sheet will be graded.
1. (3 pts) Determine the minimum number of terms of the convergent series
∞
X
n=1
(−1)n−1
3n+ 2 that
must be summed so that the remainder is less than 1
25.
(a) 8 (b) 6 (c) 5 (d) 7
2. (3 pts.) The Maclaurin series for f(x) = 1
1−xis
1
1−x=
∞
X
n=0
xn,for |x|<1.
Use the Maclaurin series for 1
1−xto determine the Maclaurin series for x
9−x2.
(a)
∞
X
n=0
x2n+1
9n+1
(b)
∞
X
n=0
x2n
9n+1
(c)
∞
X
n=0
x2n+1
9
(d)
∞
X
n=0
xn+1
9·3n
Version A - Page 2 of 12
MATH 1080
Calculus of One Variable II
Test 3
Version A
Fall 2017
Sections 11.5 - 11.11,
Appendix C, 10.1, 10.2
3. (3 pts.) The Maclaurin series for f(x) = x3cos(x5) is
x3cos(x5) =
∞
X
n=0
(−1)nx10n+3
(2n)! ,for − ∞ < x < ∞.
Use the Maclaurin series for x3cos(x5) to evaluate Zx3cos(x5)dx as a power series.
(a) C+
∞
X
n=0
(−1)n+1x10n+4
(2n)!(n+ 1)(10n+ 4)
(b) C+
∞
X
n=0
(−1)nx10n+4
(2n)!(10n+ 4)
(c) C+
∞
X
n=0
(−1)n(10n+ 3)x10n+2
(2n)!
(d) C+
∞
X
n=0
(−1)n(10n+ 3)x10n+2
(2n)!(10n+ 2)
4. (3 pts.) Which of the following statements is TRUE about the series
∞
X
n=1
3 + cos n
2n?
(a) The series converges absolutely by the Comparison Test.
(b) The series diverges by the Divergence Test.
(c) The series diverges by the Integral Test.
(d) The series converges by the Alternating Series Test.
Version A - Page 3 of 12
Document Summary
Instructions: you are not permitted to use a calculator on any portion of this test. You are not allowed to use any textbook, notes, cell phone, laptop, tablet, smart watch, or any technology on any portion of this test. All devices must be turned o while you are in the testing room. During this test, any communication with any person (other than the instructor or a designated proctor) in any form, including written, signed, verbal, or digital, is understood to be a violation of academic integrity. No part of this test may be removed from the examination room. You have 90 minutes to complete the entire test. On my honor, i have neither given nor received inappropriate or unauthorized infor- mation at any time before or during this test. Multiple choice: there are 10 multiple choice questions. The multiple choice problems will count for 30% of the total grade.
