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Richard_Exam_4_Practice_Winter_2007

# Richard_Exam_4_Practice_Winter_2007 - M A T H 2 0 3...

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MATH 203 E\-{\I -I PLE \SE SHO\\ ALL \\ ORK I I er T) h: ill: ::::.:.'.:'.:', ii::.,utSldc thc graph of r:6 and inside the graph of r: J + rlccls(O) \ \, \ a. Sketc: l:l:::-ll.rn D. tr \\:.:r ,, j. i:bie integral in polar coordinates that gives the area of D. Do not integrate. f.. I L.:: S be the solid bounded betweenthe graphs of z: {3x" +3y- andz.:3. -i Sketch the solid S. b. Write a triple integral in cylindrical coordinates that sives the volume of S. Do not integrate. c. Write a triple integral in spherical coordinates thal gir es the volr,rme of S. Do not integrate. 3. Let S be the solid bounded bctu. .cn th,-- srapli. oi'r - lr - 1z - 8 and the coordinate planes. ' a. Sketch the solid S. b. Write triple integrals in rectangular coordinates that circ: lhe r-ir,.rJilute o1-thc centero1- \ mass of the solid S if the density'at a point P(x. l.z) rn S is prtrpLrnir-n.r. t,'tire distance the point P is fiom thc origin. Do not integrate' .r. ti' +. Let D be the region bounded between the graphs ofy: - r/+ - \- .) : \. rnJ \ - rl \r. ! a. Sketch the region D. !' b. Write a double integral in polar coordinates that gives the area of D. Do not integrate . r -1 .1./i '\ 5. [:r aluatc i | [ dz tr dr dt)) n ithout perfbmring any inte gratitrrt ---_\_ :, 6. Clonsider the irttegr.r, \r" --dYdx. )) - I ! \ - + \/- a. Sketch the region of integratirrn b. Convert the integral to a double integral in polar coordinates. Do not integrate. 1. Let S bethe solidboundedbetr,r'eenthe graphsr - .'t -.t) and y:0. ,, Sketch the solid S.

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Ansrrers % rh f ), -1V" /) 4+4 cos(0) f rdrd0 J o \r\ r: {-i r 2b. 2a. The solid is bounded above by the plane z= 3 and below by the cone z= znJr l v -- i' j ,i, dz(rdrdo) 21 16 3scctQ) r sin(o) dp dQ do' v=Il I P The solid is bounded above by the plane x + 2Y + 4z=8 and below by the plane z: 0' g-x 8-x-2Y 2 +y 2ydrdyd* 'r4 tl 60 dz d;'' dx e J 0 t- 1a 3a. 3b. rdrd0 4b. A: 5a. Tlre solid is bounded above by the plane z:3 and below by the cone z = .,;- b+\ -' ' 5b -1- /2 )co'," [Jr':r *r,f df d0) ll_ % o ' 1 2' -r ^' thc lett bv the Plane 1 Thesolidisboundedontheriehtbytheparaboloidy:4-(*,+z2l,andonthelenbyt t. ) 4-r) v= J'l i dY(rdrdo)' (l 0 o 6b. 'la. '7b. +JV 8-x e-2 rf JJ 00 tn/d 2 IJ n0
MATH-203 E\{\I-I I . [-et D t'.- ths rii: . : PLE \SE SHO\\ {LL \\ ORK -i:.t:' irr- -:.1:: -: : = -' - -ls:n,f , and inside the lraph of r - I + sin(0). a. b. 4. a. \k::::: i:.: ::-. .: r- b \\: .: -, : .-: : .:::::=. :n polar coordinates iihich gives the area of D. I - :: i :- :l.c s. .lrJ btrunded benreen the graphs ofz= 18 -(rt +y2) and z : xt - )1. r \r:i--:he:.tltJ S ^ ',i :rie a triple integral in rectangular coordinates

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Richard_Exam_4_Practice_Winter_2007 - M A T H 2 0 3...

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