midterm-solutions-week4

midterm-solutions-week4 - MATH 3213 ‘ FIRST MID’I‘ERM...

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Unformatted text preview: MATH 3213 ‘ FIRST MID’I‘ERM EXAMINATION <5 ohfiowf’ October 27th, 2006 Piease Show your work. You Wili receive little or no credit for a correct answer to a probiern which is not accompanied by sufficient explanations. If you have a question-about any particular problem, piease raise your hand and one of the proctors Wiil come and taik to you. At the compietion of the exam, piease hand the exam booklet to you}: TA. If you have any questions about the grading of the exam, please see the instructor within 15 cafendor days of the examination. Name: Section: #1 1t #2 #3 ext—1 #5 :1 Total} ‘2 english328 MIDTERM 2 RADKO Problem 1. Compute 1éhe integral I m xfzfldA; where R = [0,1] x [—33]. R i 3 I -~ SE a; J -— m cm .n f f (Liz-+1 g g 9 *fi ’2’ 3 r. f m f 20/ 963.1 g g Q ’y\ w 5 W022 Emma: engiish32B MIDTERM i Radko 3 Problem 2. integrate the function flay) = y over the triangle with the vertices (0,2), (1,1), (3,2). c1 english32B MIDTERM E RADKO Problem 3. A lamina (flat plate) occupies the part of the disc 2:2 + y2 _<_ 1 that lies in the first quadrant. Its density at any point is proportional to its disance from the :Ewaxis: pm: y) : Cy1 Where c is a given constant. Find the moment Mfg of this imaging with respect to the y—axis. @5 Q 5%}. englishSZB MIDTERM Z Radko Problem 4;. Write down (but don’t compute!) the tripie integral of the form fed fef dzdmdy represenéing the volurne ofthe tetrahedron.enclosed by the coordinate planes and the plane 2$+y+zm4. 6 engiish32i3 MIDTERM 1 RADKO Problem 5. Integrate the function f (:c,y, z) = m m 3; surface 22 m $2 + yg, above the my—plane, and inside of the cylinder 332 + y2 = 1. Rggmxm: E5: é(l”;92%)§ figr'g/f 05—2 5;“ 059%! 7K: .2. f“ gig—5mm : 4 __ 3? d5)» 7??) 2' ever the region that lies beiow the ...
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This note was uploaded on 05/19/2009 for the course MATH 262211204 taught by Professor Killip during the Spring '09 term at UCLA.

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midterm-solutions-week4 - MATH 3213 ‘ FIRST MID’I‘ERM...

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