MATH 200 Study Guide - Midterm Guide: Candi Of Indonesia, Ion, Rational Number
Math 253/200, Summer Term 1 2017 Page 1 of 8 Student-No.:
Midterm 1 — May 31st, 2017 Duration: 50 minutes
This test has 4 questions on 8 pages, for a total of 25 points.
•Read all the questions carefully before starting to work.
•All questions are long-answer; you should give complete arguments and explanations for
all your calculations. Write legibly and in a coherent order.
•Continue on the back of the previous page if you run out of space or use the blank page at
the end. If you continue a problem on a different page, indicate this clearly at the bottom
of the problem’s original page.
•This is a closed-book examination. None of the following are allowed: documents,
cheat sheets or electronic devices of any kind (including calculators, cell phones, etc.)
First Name: Last Name:
Student-No: Class (253 or 200):
Signature:
Question: 1 2 3 4 Total
Points: 9 4 6 6 25
Score:
Student Conduct during Examinations
1. Each examination candidate must be prepared to produce, upon the
request of the invigilator or examiner, his or her UBCcard for identi-
fication.
2. Examination candidates are not permitted to ask questions of the
examiners or invigilators, except in cases of supposed errors or ambi-
guities in examination questions, illegible or missing material, or the
like.
3. No examination candidate shall be permitted to enter the examination
room after the expiration of one-half hour from the scheduled starting
time, or to leave during the first half hour of the examination. Should
the examination run forty-five (45) minutes or less, no examination
candidate shall be permitted to enter the examination room once the
examination has begun.
4. Examination candidates must conduct themselves honestly and in ac-
cordance with established rules for a given examination, which will
be articulated by the examiner or invigilator prior to the examination
commencing. Should dishonest behaviour be observed by the exam-
iner(s) or invigilator(s), pleas of accident or forgetfulness shall not be
received.
5. Examination candidates suspected of any of the following, or any other
similar practices, may be immediately dismissed from the examination
by the examiner/invigilator, and may be subject to disciplinary ac-
tion:
(i) speaking or communicating with other examination candidates,
unless otherwise authorized;
(ii) purposely exposing written papers to the view of other exami-
nation candidates or imaging devices;
(iii) purposely viewing the written papers of other examination can-
didates;
(iv) using or having visible at the place of writing any books, papers
or other memory aid devices other than those authorized by the
examiner(s); and,
(v) using or operating electronic devices including but not lim-
ited to telephones, calculators, computers, or similar devices
other than those authorized by the examiner(s)(electronic de-
vices other than those authorized by the examiner(s) must be
completely powered down if present at the place of writing).
6. Examination candidates must not destroy or damage any examination
material, must hand in all examination papers, and must not take any
examination material from the examination room without permission
of the examiner or invigilator.
7. Notwithstanding the above, for any mode of examination that does
not fall into the traditional, paper-based method, examination candi-
dates shall adhere to any special rules for conduct as established and
articulated by the examiner.
8. Examination candidates must follow any additional examination rules
or directions communicated by the examiner(s) or invigilator(s).
Math 253/200, Summer Term 1 2017 Page 2 of 8 Student-No.:
1. (a)3 marks Use implicit differentiation to find ∂z
∂x where zis implicitly given as a function of xand
yby the equation xyz =ex+y+z.
(b)3 marks Let z=exy +yand suppose that x=f(t) and y=g(t) where fand gare functions
such that f(0) = 2, f0(0) = −1, g(0) = 3, and g0(0) = 2. Compute dz
dt when t= 0.
Page 2
Math 253/200, Summer Term 1 2017 Page 3 of 8 Student-No.:
(c)3 marks Let z=1
2log(x2+y2) (the log here is the natural log). Which of the following partial
differential equations does zsatisfy? Clearly circle all which apply:
∂2z
∂x2+∂2z
∂y2= 0 ∂2z
∂x2−
∂2z
∂y2= 0
∂2z
∂x∂y + 2 ∂z
∂x
∂z
∂y = 0 ∂z
∂x2
+∂z
∂y 2
= 1
Page 3
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MATH 200 Full Course Notes
Verified Note
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Document Summary
This test has 4 questions on 8 pages, for a total of 25 points: read all the questions carefully before starting to work, all questions are long-answer; you should give complete arguments and explanations for all your calculations. Write legibly and in a coherent order: continue on the back of the previous page if you run out of space or use the blank page at the end. If you continue a problem on a di erent page, indicate this clearly at the bottom of the problem"s original page: this is a closed-book examination. None of the following are allowed: documents, cheat sheets or electronic devices of any kind (including calculators, cell phones, etc. ) Student conduct during examinations: each examination candidate must be prepared to produce, upon the request of the invigilator or examiner, his or her ubccard for identi- Use implicit di erentiation to nd z y by the equation xyz = ex+y+z.
