MATH 104 Study Guide - Midterm Guide: Urt, Electronics Corporation Of India Limited, Fast Fourier Transform
The University of British Columbia
10 October 2013
Common Midterm for All Sections of MATH 104 and 184
Closed book examination Time: 60 minutes
n
Lasr Nam" Sb Lo-n o N a First
Signature
Student Number
MATH 104 or MATH 184 (Circle one) Section Number:
Special Instructions:
No memory aids are aliowed. No calculators. No communication devices. 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
o Each candidate must be prepared to produce, upou request, a
UBCcard for identification.
o Candidates are not permitted to ask questions ofthe invigilators,
except in cases of supposed errors or ambiguities in examination
questions.
r Candidates suspected of any of the following, or sirnilar, dishon-
est practices shall be imrnediately dismissed from the examination
and shall be liable to disciplinary action.
(a) Having at the piace of writing any books, papers
or memoranda, calculators, computers, sound or image play-
ers/recorders/transmitters (including telephones), or other mem-
ory aid devices, other than those authorized by the examiners.
(b) Speaking or comrnunicating with other candidates.
(c) Purposely exposing written papers to the view ofother can-
didates or imaging devices. The plea of accident or forgetfulness
shall not be received.
r Candidates must not destroy or mutilate any exatnination mate-
rial; must hand in all exarnination papers; and must not take any
examination rnaterial from the examination room without pertnis-
sion of the invigilator.
r Candidates must follow any additional examination rules or di-
rections communicated by the instructor or invigilator.
118
2B
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47
57
Total 50
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10 OCT 2013 Math 104/184 Name:
[21] 1. Short Answer Questions. Each question is worth
in the box provided, but NO CREDIT will be given for
accompanying work.
/t 1 \
(a) Evaluate lim [ - - =- ].
o-+o\r rz*r/
=.4
z+,(
Page2of9pages
3 points. Put your final answer
the answer without the correct
Ansr,ver:
4
t.
\ rwr
Y$o
€-t
(b) Evaluate hm {-.
att a't - *
a-+1at - ti t^tt*
S: :vt c.n.tv,^^);#
1^-+ t t
tA.
5o \ivrn. g* = {: =O
(c) Find the derivative of f (r) :sln(brJ
r, +I
f '(r) = Cract.:)'C*{)-s;5Eqi
t eos Csx) Lx',F{) 3 \;r Csx) [zx)
GtoD'
,t vv\a{L 4r- tzt^/t f,€ p,ra(:"^-* fi'^!L
4 vu,etL &- tz^u.',u"*1. d'-ti il/e '
te,,tt vrnor-Ls P- qf,.ilm*"t' Gd,trlsUJ*e,f-
O-S
A'cD = co' (Et*D * >("!+''J
= ,l'.(tt* a) + , (t'' t*).
'{ v^axL 4t- Lln*ri^q pn.S*^ct AtJL I efu+^@t
A tptat(f-'f.- tzrrt $rtl dlatitt- /"Ja t
' (") lel 7111 : rsin(r). Find the fiuation of the tangent line to f (r) at r: rl4.
,-Jf1'-"P,5t^
ur=T *ytq)=C5;^$)
i^^,nk f:'&
( A w\^4*Ar,r.t nt*t.=
{'t*)= stin L + T eos r-
Page3of9pages
10 OCT 2013 Math 7041784 Name:
(d) Find g'(z) if g(") : z(e"" +r).
-Tt-_ _
+rlZ
,t
Ean + +or^Aa^* ,Li* t
0
Il- Xn-s-)fx-9o)
A*, e.tLl- t
gi*{'tt(','zr.f'L r-. *6$.d
IBLE n 'zv."'vL
{.- eorre-c-f
73
MATH 104 Full Course Notes
Verified Note
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