MTH 203SP06 Exam 3 - American University of Sharjah...

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Unformatted text preview: American University of Sharjah Department of Computer Science, Mathematics, and Statistics MTH 203 - EXAM III Spring 2006 Name: ID# ' Section# Instructor Name Q1. (12%) Set up triple integral in cylindrical coordinates to find the volume of the solid region in the first octant cut from the cylinder x2+y25 1, by the sphere x2+y2 + zzs 9. (Do not evaluate the integral) A 7.2 - 412/ ‘\ W V ’4 {MA/W9 02 (12%)Set up triple integral in rectangular coordinates to find the mass of the solid that is bounded above by the paraboloid z = 4 — 9x2 —y2and below by the plane z = 3.The density at P(x, y, z) is proportional to the distance from the origin to P. (Do not evaluate the integral) Hint: mass= x,y,z)dV, x,y,2) =densit . HM A v L D 3061,01?):K xzfi‘o ’Z" 352%,“? ( LIKY’tl’llg W W We? Mm; : KWJMELJK ~ )/ uqu a a? ,i ’5 g- Q3.’(4%)a) Convert to rectangular coordinates and describe the'graph‘of pcsc(¢) = 25in(67). \l Slfl<$_ fizzfsmflfmc—E' \fjd . ‘ , 1% \0/0 XL¢(9»1)?+?2:l 2 §/' VE/ f4 b)(12%)l Change to Spherical coordinates the following integral (Do not evaluate the integral): lllgltgzdmwx (Cl M We) . 0V \7/ v tan (Sgd‘ggég in 9? (Ii/W, o O 0 q ’5’ a $ '04. (14%)Find the outward flux of field F(x, y) =_ (y — 6x2)i + (X2+y)j aéross the triangle made by the linesx = 0,y = x, and = 1. ' : Flux=§ Mdy—Ndx). , y - QS.(10%) Evaluate Icyzdx +xdy + (z —x)dz, of the curve C1 given by r60: 1 i +th + t3k, 0 s t s ltfollowed by the straight line C; from (1,1,1) to (2,3,2). where C consists \ . , : ffon‘trtmum(firtJW‘a/f 61%;; V 2 $99,563itflg7/(‘t3'fia 95 C! jgétfl‘L- Lfifiw (7 0 z: 536+} 4/ fili’é‘ CL‘ [2: (Hf 0554’) ?..¢ (AL- 6’ 4494f (Q \( ){HtMv’L +6145H/0/W‘tglfi ’1 Mtg/OM . "7:!— f-f’lf > / I. S 8 3142}L%21C7$Jd}£§63+6 ¢ H” . F 3 I Cb 0 <0 1 3133/2“? juhfif 3 " é+-9<L&Zj& fvf ~ 2 j 6 C C a (l I 064227..) Let F(x, y, z) = ' (2xe2y)i + 2(x2e2y +ycot(z))j —y2 csc2(z)k. a) Show that [C F.d F is independent of path and find a potential function f for F. b) If F is a force field, find the work done by Falong any curve C from (1,0, #3) to (2, 1, 71/4). Rd 2:53 6547229 ZN?— > flaw V 1 [E M at) J; ,Mfl QOMMMzKe ? / 2 x f alcgvz/gv998h3/"19 4 E ‘— 11) ill/39¢: 1,5 hf?) g We exam?) «E C f{X¢w,I?—j)2 K C ...
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MTH 203SP06 Exam 3 - American University of Sharjah...

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