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Unformatted text preview: Multiple choice questions .[5_ points each]. A score of +1 will be given if no answer is marked. No calcuietors are
allowed on this exam. Please show all work that you wish to he
considered for partial credit and circle the letter correaondjng
to your choice of answer. 1. The value of o: for which the vector v 2 —6i + ocj + 3k is parallel
to the plane 2 = 2s — 53; + T is given by: (530 M wwmsﬂ I: he {235:4}
(b) We —
@3 .30 0:\/ Lo“. 2: —],Z '§u{ "3
Lil
(d) 12 o" :53: :1“! 01:3
{e)15 2. Let v = (1,21 0} and u = (—2, 1,3}. The angle between 11 and v
is: (5)3
(1345" J— ; : t —2 + 2.3+ 93 :0
(eyes .5:
(gm? Ms:0
[e)180° ‘3 .
92:30 3. The surfsee p = ees s5; sis2 s; can be described in cylindrical coor—
dineteeas: {V g =Joﬂmsp " :j am"?
{b}32+y2=3\/—($2+92)/32 f EfIP/e e
{C)T=P/r' fee4‘13: w'P/m:e> .2: = 1.2 . Ir ﬁnk;
(e) none of the above 'I r. : ELF... . ll“
' x, (a) r = zeotﬂ Flt? 4. The road on which you are driving curves to the left. You gently
3.13131}r the brakes. If you use “12:00” for straight ahead, “3:00” for
t‘lireetlllrr to your right and so forth, the direetion of your accelera— tion could beet be deeerib$ 113$: tr l 1“ 1‘” M” (a) 12:00
{b) 2:00
(o) 4:00 [2 points per ﬁgure] For each of the three pictures of real objects,
choose the letter of the equation which best represents the object.
Note that the equations are in various coordinate systems and may
describe the object in an},r scale and orientation. Figure 1. an apple core [top and bottom are rounded}= a fruit roll—up spiraﬂing on a
table, and a whisk [describe the wire part, not the handle} X. (a) p25' Wéwww Jami41am:
(b) s =r = 9,8 <_‘: 20 a 3193111.? cmw’aﬂ u’ﬁ mﬁﬂh/éégm LIEU—{em
X (c) 2: £ $2+y2 5 E octagonmien; part oi L uﬂtmoiojr (d)r=9,0£s£1,0£9$38 # rsﬂ‘i‘ﬁ *r’ipeﬂ Might 1, (6)981!”in 5 5 )2 s f a», a. {3166 f
nine? :5 i a». a Livonia” Equation for core is which letter? 61. Equation for fruit roll—up is which letter? ei Equation for whisk is which letter? g 6. Let 11%) he a smooth curve {s(t),y(t),z(t}} for 1 g t g 3. Which
of the following statements is true? (Only one is true.) {a} ff ﬁt} dt ie the distance between to) and 113). (h)  ff 1" (t) dr is the length of the curve traced by r[t)
fromtz 1 tot=3. (c) L3 Jr’{t) dt is the distance between r(1) and r(3). @ f13r’(t)dt is the vector between to} and 1(3). B3 ‘6th ”FMﬁﬁmm‘gmﬂ marten J Lag/m dew”
M” (Eocene/{L LEVU3, {Re JiAPEMLMEm’? Vic/£701"
rig}  r I n «Britt152s to fr‘ melt '1’. Circle the letter [HQ—(E) corresponding to the vector whose cross
product with the vector V has the greatest magnitude. All vectors
are parallel to the plane of the paper. h M {3'4 height Siltkw {en la wziﬂwtft‘ke RMwﬂf 22", IE " fixer: Hider 92¢ miﬁgmaﬁ bite/3.111%
4 r
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:14 m 39..L.M.£ SFﬁLLE‘. Hurbiﬂ_ LNJL 5.612. {kg/f 5‘1! :5 3. MIX} RAH l..— a. gimmoﬂkrog mwp«hifw dun/M TUE}: 9"“ t r— 554.75, mﬁf} EarH —_'—_— 1
’ ’ W :ﬁ(r¢h 1‘, EMEJJ. EEK“; (L920! :Q‘rﬂlrﬂh‘r “#:5er F4 Answer (0; 3'? if ) dti' 9. [5 points] Compute the eeeuleting plane at the point (e1 1,1) to
the enrve r{t)=(e*,t,1jt} .
We knew {Lu/4 rr'Hi' [DEM innu. MLLLCA‘HMJ Payee (eCLEELFlf?nu
1‘4 subway/3 {Ht ﬂu! MW'K‘Ety my. J in a. WMELE winter: {a
“WK“ ‘3‘“ 5" LMJ’W M F"!!! 1 WWI: (ﬂit—{jﬁetﬂ'ﬂ‘g};
= (2 {'1 *Ede‘r—Nﬂei a“ ). em Framer,” £91 we WMJ um :25 [£}~BEF€)_ 3(3)th Feline El} 949% Am. JX—ﬁejnehotrq
amﬂ Piagn‘wa {H 'ffqunLVJ {61m} Lu“! 3/4 {E3€£+ 4:0 =10P:,2€_ Answer: EXSﬁgEE +38 :{5’ «1r [8 points] The canopy covering the tables at Gutmannfest 200’? is fastened to the tops of two trees, one located 2'20 feet East of the podium at a height of 75 feet, and one located 320 feet North of the podium at a height of 50 feet. The third anchor point of the canopy is on a ﬂagpole next to the podium and may be raised or lowered to any height. How high must the third ”int be in order that the wind which is blowing horizontally from the Northwest owl be blowing parallel to the plane of the canopy [thus minimizing
$111, the chance of it being torn by the wind)? M
w_\ {111}. H.43l TEA}; F‘LAFK’EUM L”) 11¢ 4?an P’EﬂWEH'FCLFDufll
l P51051059) Mr P141120, loaf/smile [3&an 3
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llrho  with “UL a 94th
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N 14 31cm 6}} “5+ L‘a*‘Q:0 3’11.“ P 1’1 “mph“! 0+320+91§0+1ftﬂ h J: "53502 The. Ew'l'erdec/flw corﬁ, 1mg Eﬂﬁﬁ
a», more” cm»? 0+O+Har1".10=0 =1 eazs‘zozt— :30. Answer: [8 points] A ball is ﬁred upward from the ground at an angle
3 from the horizontal and a speed of 28 meters per second. It
travels until it hits a large vertical wall 20 meters ahead (er hits
the ground ﬁrst). What angle 3 maximises the height at which the
ball hits the wall? Give your answer by stating the value of ten 9. 15—123 l' f f,iel=U‘eoaQ_mfjfslrfetu9
3
Kit): ”atoll! = Fmﬂrf=2cftm9 {Jaltltﬁafﬁl‘t‘ngzL :ZéaEvjﬁ'hﬁ— ijl‘il
mile. 1.112 jet/m em “9:10 Mo! was; a. [W W “new 3H” 59 20:26.me “if
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 Spring '07
 Temkin
 Calculus

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