MATH 41 Midterm: MATH 41 Stanford 12Exam1
15 Feb 2019
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Department
Course
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Math 41 First Exam — October 18, 2012
Name: SUID#:
Circle your section:
Valentin Buciumas Jenya Sapir Li-Cheng Tsai Dan Jerison
04 (1:15-2:05pm) 02 (1:15-2:05pm) 06 (1:15-2:05pm) ACE
09 (11:00-11:50am) 03 (11:00-11:50am) 10 (11:00-11:50am)
•Complete the following problems. In order to receive full credit, please show all of your work and
justify your answers. You do not need to simplify your answers unless specifically instructed to do
so. You may use any result proved in class or the text, but be sure to clearly state the result before
using it, and to verify that all hypotheses are satisfied.
•Please check that your copy of this exam contains 11 numbered pages and is correctly stapled.
•This is a closed-book, closed-notes exam. No electronic devices, including cellphones, headphones,
or calculation aids, will be permitted for any reason.
•You have 2 hours. Your organizer will signal the times between which you are permitted to be
writing, including anything on this cover sheet, and to have the exam booklet open. During these
times, the exam and all papers must remain in the testing room. When you are finished, you must
hand your exam paper to a member of teaching staff.
•Paper not provided by teaching staff is prohibited. If you need extra room for your answers, use the
back side of a page or one of the extra sheets provided in this packet, and clearly indicate that your
answer continues there. Do not unstaple or detach pages from this exam.
•It is your responsibility to arrange to pick up your graded exam paper from your section leader in
a timely manner. You have only until Thursday, November 1, to resubmit your exam for any
regrade considerations; consult your section leader about the exact details of the submission process.
•Please sign the following:
“On my honor, I have neither given nor received any aid on this
examination. I have furthermore abided by all other aspects of the
honor code with respect to this examination.”
Signature:
Math 41, Autumn 2012 First Exam — October 18, 2012 Page 1 of 11
1. (12 points) Find each of the following limits, with justification. If the limit does not exist, explain
why. If there is an infinite limit, then explain whether it is ∞or −∞.
(a) lim
x→12
x2−1−1
x−1
(b) lim
x→−2+
xln(2 + x)
x2+ 2x+ 2
Math 41, Autumn 2012 First Exam — October 18, 2012 Page 2 of 11
(c) lim
x→0(sin2x) 2cos(1/x)
Document Summary
Math 41 first exam october 18, 2012. In order to receive full credit, please show all of your work and justify your answers. You do not need to simplify your answers unless speci cally instructed to do so. No electronic devices, including cellphones, headphones, or calculation aids, will be permitted for any reason: you have 2 hours. Your organizer will signal the times between which you are permitted to be writing, including anything on this cover sheet, and to have the exam booklet open. During these times, the exam and all papers must remain in the testing room. When you are nished, you must hand your exam paper to a member of teaching sta : paper not provided by teaching sta is prohibited. If you need extra room for your answers, use the back side of a page or one of the extra sheets provided in this packet, and clearly indicate that your answer continues there.
