Math 1320.001 Exam 03
Fall 2015
OflS
Naiiie
Class Nitniber:________________
Stmlent ID Nmnl )er:
Inst rll(t bus:
o
Please remove lieadplioiies amid hit 5
o rUle scheduled t 111w for
tins
t he
exam
is 8:35am 9:25am. You will be given
your saint ions. Your eain imist be sub—
exam
an additional 5 huh to finalize
nutted proiiiptly at 9:1Uaimu.
dimriiig
—
begmniiig, read t lirougli t he exam. It is recouuimended that you
wit ii the prohleiius you. are most. (oluhdellt about solviug.
o I3efore
begin
O
I will not answer quiestiomis (hiring the exaiiu. If you believe there is
a typo iii t lie exaimu nuake a muote on t he jnobleiii and do youm’ best to
(leliH)iist rate your iuiderstandiig of the ideis I )eiig tested.
work, as partial credit will be given where appropriate. If 110
work is shown, you may receive a score of zero for the problem.
• Show all
o
All final answers sluoimM he written in time space provided oii the eXam
aud iii siniplified form unless noted otherwise.
• CALCULATORS ARE NOT ALLOWED ON THIS EXAM
• This is a ‘closed iiotes/closed book’ (‘Xlfll You are not allowed any
outside aids (luring this exam. If you. have papers at your (hesk (luring
the exam you will be given a zero on the exam.
—
• If your phone is out during the exam it will be considered a
cheating offense put your phone away!
-
Mat h1320.UU1
Exam 03, Page 2
of
11
04
December
201
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103
Score
103 J)OilltS but will be graded out of 100 p0111tH. This gives each
stuideiit the oI)portuullity of a. 3 point bollus.
04 December 2015
Exam 03, Page 3 of 11
Mathl32O.001
WRITE YOUR ANSWERS IN THE PROVIDED BOXES
SHOW YOUR WORK
[6
points]
1. Given the points P(1. 0,1) and Q(2, 3. 1),
mpc--o 1-&nW<
‘-
(a) Write the vector ecluation for the line segment that joins P and
oecfor
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frvçn
or rn
is,
i
Q.
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U r<
Ct
•Um orLt
(b) Write the
parametric equations for
the line segment.
kniu ftrnekflt
4?txrn
o”I
[3 points]
2. Find an equation for a plane containing the point (—1, 5, 1) and perpendicular to the
line r(t) =< 2, —3,0 > +t < 1,2,—i >.
K:
Yec{-o- Inhe dtcbon
ec fmr
pocni (
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Math 1320.001
5p
D1\Jcr
b
(b) \Vrite this equation
much as possible.
CnuerOfl
Ofl
spherical coordinates. Simplify the resulting equation as
Jce
pcsCQ
Cmpc -fo Hm
ei
Tfhc
& #
2
ip
arc4-ctn(’1&
(c) Sketch 4 level curves for this surface on the same plot ailci label each curve with it’s
&fi
pa. i.e
correspoiiding height.
--
-4-yjjjr
..
kL1LJ:øA
•ckov.s
or
Cr
I
.Q-cr
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or
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r
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0
crc-L
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2
t3p2n
jJTT)(, 300
pcc.42
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04 December 2015
Exam 03, Page 5 of 11
c..or tflrC
ctti-
-r
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r
(I.e.
-wn sp-cLd
Oofla,lfnc.
C(c-LL’&
çc n t cp#.-uct
(ci) What type of quaciric surface does tins equation describe? Draw a sketch of this
surface.
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j2
uI
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Z.=
2
iLC3iZC
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Mathl32O.001
[10 points]
7. Given
5t
Exam 03, Page 7 of 11
f(x, y)
3 + 8:y
y
5
x
3+
i
04 December 2015
-k Yuii_or/<
/ 3 # i6 / &7
C.in 4-
+ 1,
(a) Calculate f(c,y)
’k
kr ,&o)* 7
)
t
A pa r4i-€
4tm i,ui’ô/o;p
7
oI
dt
cf 1rrnS
iliL)
(Ii) Calculate
a
pt’
I- ,777S
,[)
17OIOj’
(efl
[9 poiits]
8. Giveii z
de-
siu(x + 4y), x
=
L, and y
2
e
= ,
calculate
/1.5 ,3
‘>
cz
2e
•
=
d
(2e2
•de2t. 2e
\V
cos(ett*)[2e.
_t’
t
[9 points]
9.
(t?pfs
kj
Given
04 December 2015
Exam 03, Page 8 of 11
iViat 111320.001
the surface described by: z
emp6C 1t
=
(a) Find an equatioll for a plaiie tangent to z at the
pomt
jjjz(/(
/J
j
1
j•4
(1, 4, 3).
:
Uonrrn:
a
Pirt
(1)4,
(YO)z(;)=
)
r
•
•
fx ()
)
CLJjte
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2
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=
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(x
i.jvi )fr2ô)
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t
oppfl
31-
=
(b) A1NH’oximate the value of
z
at (‘
)
=
z
1
Compi
(1k, 3)
,uc,-K
,,
7
,,4
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fl fl
fl
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a
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Mathl32O. 001
Exam 03, Page 11 of 11
04 December 2015
[3 points] 11. The following figure depicts four representations of the Tangent-Normal-Binormal frame
orientation. Which of these representations is correct?
In each figure, both wheels depict the same vector orientation, with T = Tangent Vector,
N = Normal Vector, B = Binormal Vector and the curved arrow indicating the direction
of the wheel’s movement/position pararneterization. The circle outlined in white indi
cates that the binormal vector is coming out of the page and the absence of the circle
indicates that the binormal vector is pointing into the page.
C
D
-r
C
in ‘1t d/,ccJ7,r)
%Cr)
2
(
C,n/cx
N L (rn4QQ Ifl 1 ci
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