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Unformatted text preview: Vincent (ij777) — FINAL Review w Gilbert "— (57495) 1 This print—out should have 22 questions. Multiplemehoice questions may continue on the next column or page — ﬁnd ail choices
before answering. 001 10.0 points I
Use the transformation
T = (ua 0) ~+ (it, y)
with
:1: = 4n ~i— o, ymévmu to evaluate the integral Im/V/waimwdmdy when D is the square with vertices (0,0), (1,4), (5, 3) (4,—1).
1. I m 85
2. I =17
3. I = 16
4. Iwﬁéi
5. I = 68
6. I = 80 002 10.0 points Describe the motion of a particle with posi»«
tion P(;I:, y) when a: = 58int, y m Zoost as t varies in the interval 0 S t S 271'. 1. Moves along the iine __ nml
5+2 ’ starting at (5, 0) and ending at (0, 2). 2. Moves once counterclockvVise along the
ellipse
(War we2 = 1, starting and ending at (0, 2). 3. Moves along the line a: yw
5+2WI’ starting at (0, 2) and ending at (5, 0). 4. Moves once clockwise along the ellipse 2 2
9:491:15
25 4 starting and ending at (E), 2). 5. Moves once clockwise along the ellipse
(5:02 + (2102' m 1,
starting and ending at (0, 2). 6. Moves once counterclockwise along the ellipse 2
2
e. in I 1,
25 4 starting and ending at (0, 2). 003 10.0 points d2
Find 33% for the curve given parametricaliy
by
:1;(t) : 4+9, 31(13): 29w?
1 its m 3':
c5222 at
2 z e
‘ 053:2 3
3 its : 3':
. (£332 316
4 die m .9:
(1322 2t
5_ @321 m Which of the following expressions are well— vinoent Univ???) m FINAL Review — Gilbert ~' (57495) 3 007 10.0 points 7’. none of them 8. I and III only deﬁned for all vectors a, b, c, and d? I.
II a><(bc),
III (ab)>< (cd). 1. Which of the following statements are true for 009 10.0 points lal><(b><<=), A line 2 passes through the point P(2, l, 3)
and is pazallel to the vector ( 1, 4, 3 III only pl 8:: f:rvhet point Q does 8 intersect the my—
Ianci III only 1, Q(—3, 1, 0) land II only 2. Q(0, 5, 3) II only 3. Q(3, 5, 0) II and III only 4, Q(0, 3, —3) Ionly 5. Q(0,1,5) all of them 6. Q(1, ~3, 0) none of them 010 10.0 points 008 10.0 points The curve of intersection of the surfaces
shown in all lines and planes in 3—speoe? 1. two lines perpendicular to a third line are parallel, II. two planes perpendicular to a third plane
are parallel, III. two lines parallel to a plane are parallel. 1. all of them II and III only
I and II only II only III only I only Vincent (jmv???) w FINAL Review w Gilbert m (57495) 5
at the point PG), 2). 017 10.0 points 1. max slope m: 47?
Find the maximum volume, me} for a 8 rectangular solid in the ﬁrst octant with one
vertex at the origin and one on the plane I! 2. max slope 3. max slope m 271' 33 y Z
6— + + a = 1.
4. max slope m 2
8
5. max slope 2 8n 1. Vmw = 3); cu. units
6' max SlOpe = 7r 2.1/me m 3 cu. units
7’. mexslope x E 26
3. me : m cu. units
8. max Slope = 4 9
25 .
016 10.0 points 4 Vmax m 3 cu.un1ts
A rectangular box 28 
, i , n 5. Vmw = 3; cu. units 018 10.0 points Reverse the order of integration in the inte
gral 4 1 ‘
I =/ / ﬂwayldy dx,
3 «5/2 with no top is to be constructed having a but make no attempt to evaluate either 1nte~ volume of cubic inches. What width 3:, in gml' inches, will minimize the amount of materiai 1 4y2
to be used in its construction. (Assume no 1_ I m f / ﬂag, y) arm dy
material is wasted.) «5/2 3
. . J37? 4x2
1. Wldth = 41IlChGS 2' 2 f f d2; 0 3
2. width W Zinches 1 3
3 I e f ( H31, yldw) dy
\fé/ra 2y? 3. width m 5 inches
«3/2 2
4. I m f ( ﬂan, y) alas) dy
G 4. wisth 992 H 3 inches
. 2 ‘1 2y
5.! = / / f(3:,y)dz dy
"5. width 1 inches _ Jig/2 3 Vincent (jmv???) — FINAL Review ~ Gilbert w (57495) is the unit cube having one corner at the
origin and the coordinate planes for three of its feces.
Find the cosine of the angle 6 between DA
and DC.
1
1. = w
0036 2 "I
2. cost} m [3%
2
 1
3. c039 m ——
\/§
1
4. cost? m e
\/2_
5. cost? = 0
2
6. 6 m ——
cos 3 ...
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 Fall '09
 Gilbert

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