This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MAT293F VECTOR CALCULUS
Quiz 1
1 October 2007 10:05 am  10:55 am Closed Book, No aid sheets, No calculators Instructor: J. W. Davis Last Name: \5 KO \ )CELU'l 8
Given Name: 2‘ U—‘R 0142's . Student #: FOR MARKER USE ONLY Note: The following integrals may be useful. fcoszede = 1(t) + lsin20 + C; fsinzﬁde 2 l0 — lsin26 + C
2 4 2 4 Page 1 of 7 1) a) (3 marks) b) (5 marks)
Ls Evaluate [24]:xe + y2)dydx .4
Lt 1
a) z w] w (MW—w
z 2.
3 4
7L é (g4 iL__32_Z _ LL51
‘1}:‘3T‘L3L’ 2—(‘3*3 .3 E)” 3 Evaluate J. x "MdR ,Where R is the region in the 1St quadrant bounded by the parabolas
R
y = x2 and y = 4  x2. Sketch the region of integration. pare Lear M“; w a“ Page 2 of 7 2) Find the volume that lies below the paraboloid z = r2 and above one loop of the lemniscate r2 = 2 sinQ . Provide a sketch of the volume. . (6 marks) ‘5 '1: 'q
0
a
J T
" 9...}. lkle us If
H a 7. Page 3 of 7 3) 1 a) Evaluate IV xysinde where V is the volume deﬁned by: 0 _<x _< 72‘, 0 _< y 5 7r, 0_<z_<zr. "IF
.'IT 1T 11‘ ‘p—
TY ... 1.  L
(3 marks) j yogiu, j 3&1 5 6iw‘bflZ', = L25: I [iii 1 [— {mijg
b 0 0 P 0 0
Z. 'L 4
4 E If, (HA == E.
L 2 b) Use Spherical coordinates to ﬁnd the mass of a ball bounded by x2 + y2 + 22 S 4 ifits density is given by l(x,y,z) = x2 + yz. (7 marks) aL= smug/Cm? x1+31_ St 51.13";
3‘39“?! 52M?
7—1? TV I a Tr L \ ”S
H‘ 549 i «awful SJ§ ‘ Qwiﬁli‘m’i)"‘“’wl%
6i__17”"_(_m?4+ Cm?(]r _ gin—(173:)
S T 0 ' 5 3
ZSéTF Page 4 of 7 21;, km) 5T 32T 4 Sh hT tz— ”2a" 1' hDh ‘:—=
) owt at (x,) J; 06 Vlsaso utlontotel eatequatlon é’t kﬂzx
(6marks)
45;..—
1T. 15"”? UL
I We) = 3'} J a.“ JV
0
5/7. u. x i
9: _ LL: e  3‘3 3 r“ (“2—) JD
3% d’ﬁ—A \FP #kt h' —  9c To '3’? 474.63:
1 r17. 5
.ﬂ. ,1)“ l/Lt “r xl/let \ __’_:_. a /
9:: : L'3 c _____.. r H
$09 JIF‘ 2' ”Lt JW‘L‘L”
3:: L if” :22.  ”d” 1/1 51"" Wu:
3L1. * Jﬁ: 41w aJﬂm 1 ”A 41% g ‘1 L: ‘_ “x ‘7 1;: c 4: = _:
9K), # 2. “Th. Qt Page 5 of 7 3 3
5) Find the surface area of Z = xA + yA in the ﬁrst octant cut off by the planex + y =1, by
means of a double integral over the projected area. (8 marks) 1. W 9. “1 3:3
. ‘ 512
=g%(ﬁ\ m Z‘g‘é—(Qr‘ ﬂ.) (“ "*5 ) Page 6 of 7 6) Find the location of the centroid of the volume in the ﬁrst octant bounded by the plane
x + y + z = a. Sketch the volume. (10 marks) "L —— 034 4 o.
 7C 1: '— . '—3 g. __
14 a “l :7 Bj 97/191,145“: 73 =3; 7";  ‘3 Page 7 of 7 ...
View
Full Document
 Fall '08
 J.Davis

Click to edit the document details