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Course: IMA 2263, Fall 2009School: Minnesota
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2263 Math Fall 2008 Midterm 3 November 25, 2008 Time Limit: 50 minutes Name (Print): Student ID: Section Number: Teaching Assistant: Signature: This exam contains 6 pages (including this cover page) and 5 problems. Check to see if any pages are missing. Enter all requested information on the top of this page, and put your initials on the top of every page, in case the pages become separated. Calculators may be...
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2263 Math Fall 2008 Midterm 3 November 25, 2008 Time Limit: 50 minutes
Name (Print): Student ID: Section Number: Teaching Assistant: Signature:
This exam contains 6 pages (including this cover page) and 5 problems. Check to see if any pages are missing. Enter all requested information on the top of this page, and put your initials on the top of every page, in case the pages become separated. Calculators may be used. Please turn o cell phones. You may refer to your crib sheet, a half page on one side. Do not give numerical approximations to quantities such as sin 5, , or 2. However, you should simplify cos = 0, e0 = 1, and so on. 2 The following rules apply: Show your work, in a reasonably neat and coherent way, in the space provided. All answers must be justied by valid mathematical reasoning. To receive full credit on a problem, you must show enough work so that your solution can be followed by someone without a calculator. Mysterious or unsupported answers will not receive full credit. Your work should be mathematically correct and carefully and legibly written. A correct answer, unsupported by calculations, explanation, or algebraic work will receive no credit; an incorrect answer supported by substantially correct calculations and explanations might still receive partial credit.
1 2 3 4 5 TOTAL
15 pts 15 pts 20 pts 25 25 pts pts 100 pts
Math 2263 Fall 2008
Midterm 3- Page 2 of 6
November 25, 2008
1. (15 points) Let B be the box, or rectangular solid: 0 x 2, 0 y 1, 0 z 3. Find (x2 + y)(x z 2 ) dV.
B
Math 2263 Fall 2008
Midterm 3- Page 3 of 6
November 25, 2008
2. (15 points) Let E be the cylindrical solid x2 + y 2 9, 0 z 1. Find zex
E
2 +y 2
dV.
Math 2263 Fall 2008
Midterm 3- Page 4 of 6
November 25, 2008
3. (20 points) The set E in R3 is described by the inequalities: x2 + y 2 z 9 x2 y 2 .
(a) (5 points) Write a description of E in spherical coordinates.
(b) (15 points) Compute the volume of E.
Math 2263 Fall 2008
Midterm 3- Page 5 of 6
November 25, 2008
4. (25 points) Let C be the circle x2 + y 2 = 100 in the (x, y)-plane, oriented counterclockwise. Find (2xy + ex ) dx + (x2 sin y ...
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Minnesota - IMA - 2263
Math 2263Fall 2008Midterm 3, WITH SOLUTIONSNovember 25, 20081. (15 points) Let B be the box, or rectangular solid: 0 x 2, 0 y 1, 0 z 3. Find (x2 + y)(x z 2 ) dV.BSOLUTION:3 1 0 0 x4 4+yx2 25z 3 11 3 9 z z=02 2 3 2 2 2 B
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Minnesota - V - 141
CONTENTSForeword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Foreword Preface A general-purpose shared-memory model for parallel computation Vijaya Ramachandran
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Minnesota - V - 135
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Foreword Preface Iterative substructuring methods for spectral element discretizations of elliptic systems in three dimens
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Minnesota - V - 146
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Minnesota - V - 123
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M odeling 3D Object sAut hor 's Example:View t he aut hor 's code for :Tesselat ionExample.java Tesselat ionBWExample.javaCr eat ing differ ent t esselat ions /transformation groups (for positioning). Sphere[] spheres = new Sph
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CG T IPS AND T RICKS F OR AND B Y CG P ROFESSIONALSI SSUE 8 Disney Enterprises, Inc., and Walden Media, LLC. All Rights Reserved.DIGITAL ARTISTS BRING THE TIMELESS CLASSIC TO LIFEIssue 8 $10.95 USD $13.50 CanadaFE ATURE S TO RYFE ATURE S