MATH 104 Midterm: MATH 104+184 2012 Winter Test 1
The University of British Columbia
Final Examination - December 5, 2012
Mathematics 104/184
Time: 2.5 hours
LAST Name
First Name Signature
Student Number
MATH 104 or MATH 184 (Circle one) Section Number:
Special Instructions: No memory aids are allowed. No communication devices allowed.
No calculators allowed. Show all your work; little or no credit will be given for a numerical
answer without the correct accompanying work. If you need more space than the space
provided, use the back of the previous page. Where boxes are provided for answers, put your
final answers in them.
Rules governing examinations
•Each examination candidate must be prepared to produce, upon the request of the invigi-
lator or examiner, his or her UBCcard for identification.
•Candidates are not permitted to ask questions of the examiners or invigilators, except in
cases of supposed errors or ambiguities in examination questions, illegible or missing material,
or the like.
•No 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 candidate shall
be permitted to enter the examination room once the examination has begun.
•Candidates must conduct themselves honestly and in accordance 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 examiner(s) or
invigilator(s), pleas of accident or forgetfulness shall not be received.
•Candidates suspected of any of the following, or any other similar practices, may be im-
mediately dismissed from the examination by the examiner/invigilator, and may be subject
to disciplinary action:
(a) speaking or communicating with other candidates, unless otherwise authorized;
(b) purposely exposing written papers to the view of other candidates or imaging devices;
(c) purposely viewing the written papers of other candidates;
(d) 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,
(e) using or operating electronic devices including but not limited to telephones, calcula-
tors, computers, or similar devices other than those authorized by the examiner(s)–(electronic
devices other than those authorized by the examiner(s) must be completely powered down if
present at the place of writing).
•Candidates must not destroy or damage any examination material, must hand in all ex-
amination papers, and must not take any examination material from the examination room
without permission of the examiner or invigilator.
•Notwithstanding the above, for any mode of examination that does not fall into the tra-
ditional, paper-based method, examination candidates shall adhere to any special rules for
conduct as established and articulated by the examiner.
•Candidates must follow any additional examination rules or directions communicated by
the examiner(s) or invigilator(s).
Question Points Score
1 45
2 13
3 10
4 10
5 10
6 12
Total: 100
Page 1 of 14
1. (45 points) Short Problems. Each question is worth 3 points. Put your answer in the
box provided and show your work. No credit will be given for the answer without the
correct accompanying work, except for multiple choice questions.
(a) Compute lim
x→0
√x+ 1 −1
x.
Answer:
(b) For what value of the constant ais the following function continuous at x= 1?
f(x) =
xex−ex
x2−3x+ 2 if x6= 1,
aif x= 1.
Answer:
(c) Differentiate the function
f(x) = (x+ 1)cos x
.
Answer:
Page 2 of 14
(d) Let h(x) = ef(x)+ [f(x)]2where f(1) = 2, f′(1) = 5. Find h′(1).
Answer:
(e) Sketch the graph of a continuous function f(x) satisfying:
lim
x→0−
f′(x) = 1,lim
x→0+f′(x) = −1, f(0) = 3
.
(f) Let y(x) = erx. For what value of rdoes y(x) satisfy y(x)′′ −4y(x)′+ 4y(x) = 0?
Answer:
Page 3 of 14
73
MATH 104 Full Course Notes
Verified Note
73 documents
Document Summary
Show all your work; little or no credit will be given for a numerical answer without the correct accompanying work. If you need more space than the space provided, use the back of the previous page. Where boxes are provided for answers, put your. Put your answer in the box provided and show your work. No credit will be given for the answer without the correct accompanying work, except for multiple choice questions. X + 1 1 x (a) compute lim x 0. Answer: (b) for what value of the constant a is the following function continuous at x = 1? f (x) = xex ex x2 3x + 2 a if x 6= 1, if x = 1. Answer: (c) di erentiate the function f (x) = (x + 1)cos x. Page 2 of 14 (d) let h(x) = ef (x) + [f (x)]2 where f (1) = 2, f (1) = 5.
