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Math220-Sum11-Exam#3-So

Math220-Sum11-Exam#3-So - Math 220-9809 Summer 2011 Exam 3...

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Unformatted text preview: Math 220-9809, Summer 2011 Exam 3-July 25, 2011 Page 1 of6 Name: 5 6‘ [aim m S Signature: Math 220: Multi—Variable Calculus Exam 3—— Monday, July 25, 2011 Instructions: 1. Clearly print your name and sign your name in the space above. 2. There are 5 problems, each worth a specified number of points, for a total of 45 points. 3. Please work each problem in the space provided. Extra space is available on the back of each exam sheet. Clearly, identify the problem for which the space is required when using the backs of sheets. 4. Show all calculations and display answers clearly. Unjustified answers will receive no credit. 5. Write neatly and legibly. Cross out any work that you do not wish to be considered for grading. 6. Calculators may be used but all of your answers must be justified. Also, all derivatives and integrals are to be found by learned methods of calculus. 7. The following table is strictly for grading purposes. Please do not mark. Math 220-9809. Summer 2011 Exam 3-July 25, 2011 Page 2 of 6 1. Evaluate 2xy dA, where D is the triangular region with vertices (0, 0), (1, 2), and (0, 3) D (a) Sketch the region D. (0)3 7’33 fix (b) Write the region D in proper set notation. D:{(w 090.41)- 2x4. Yé 3&4? J; 3AM Above, (0) Evaluate the integral. ___"_—___—fl_,—___—_w__.__—.__—.H.———— Math 220-9809, Summer 20] 1 Exam 3-July 25, 2011 Page 3 of7 f“ 2. Use polar coordinates to find the volume of the solid Wm inside the W Lem/NS Flt/(C, x2 + y2 + 2:2 = 16 and outside of the cylinder x2 + y2 = 4 . (a) Sketch the region of intersection in the xy-plane. ’Tlnc Sf’laang xl—FYz-l-er—lé I‘m-lcrch-(s “ILL; X)” (P/anc "La/Lax 25‘0- SQ) X14 725- ’6. I'm XV f/anc w¢ («w/g; UJCZ Wam'l’ Veafam qéxz—Hflé Ié (b) Write the region of integration in proper set notation. (i.e. R = [(r,t9)| a S r S b, (x S r S [3]) {Zzé’fl/afl zgrgq) 03 a; 277} (c) Set up a double integral and evaluate it and give the exact answer. vafi W144 njflf teem/6 R 0 , A ‘2 f S‘Hr(/6H(Z)VZCIV 0 7, 3 : elm (/é— r2)%j: Math 220-9809, Summer 2011 Exam 3-July 25, 201] Page 4 of5 A 3. Find the surface area of the part of the surface 2 = xy that lies in the cylinder x2 + y2 = 1. Lara—é flywhxy. [Mt-HA XZ—Hzél- fxzy) [Y:X ‘ 277 I I u ' 2. .__ 7“ er a 9 A(g,):fimg,4, £9 55477:]: c D , 3/ “ii ISZqTf-éi' (HAL—L) 2 {to A6 0 ._.,. gjng (zd’Z‘JDJQZZgQJZ—J) +z2 4. Evaluate 6W”: 2a'V , where B is the unit ball B = {(x,y,z) | x2 + y2 + z2 5 1} . H Le-F US~ USQ SFL'CHCC/ti (oo‘rchna‘grj 81;“) 9) g)\ 0454.1) oéaézfi‘goéflg’rrf Math 220-9809, Summer 20] 1 Exam 3-July 25, 2011 Page 5 of5 5. Use the transformation x 2 Zn, y = 3v to evaluate the integral x2 dA, where R is the region R bounded by the ellipse 9x2 + 4y2 = 36. (a) Find the Jacobian of the transformation. 009)”): Z 0) :6 004/ V) O 3 (b) Find the image of the region R under the transformation. {for Msrflavma‘ffon 4X24 LI YZA fl? - " (c) Use the transformation to change the integrand. (d) Evaluate the integral. SS XQcM: (340(2) (6) Jaclv [Z a24uzdl 3&5 224 a? clouJV Chaij/LO Polar (om-eralcs aux/2w 2/“, (jg:\’(059/ VSYZSMOV S S (M rszeyclfcla 0 _ a Z 3: 2q(5fl(0529 J€)(SIV30/r):2¢l[ll9lzjjsw old; 0 o : Morel—fie? ...
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