# PracticeTest1Exam1(Section01)(2) - UNIVERSITY OF WINDSOR...

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UNIVERSITY OF WINDSOR DEPARTMENT OF MATHEMATICS AND STATISTICS Vector Calculus 62-215-01 Midterm Exam 1 Thursday, June 4, 2016 Last name (PRINT): First name : Student No. : Section No. : Instructions : This test has 8 problems and a total of 7 pages, including this cover page. You have 80 minutes. Read carefully and answer all questions. Show all the work. No calculators, cell phones or other electronic devices are allowed. Work all problems in the space provided. You must give exact answers (and not decimal approximations).
Question Points Score 1 6 2 6 3 3 4 3 5 3 6 3 7 3 8 5 9 6 10 30 11 6 12 6 13 2 Total: 82 Page 2
1. (6) Sketch and identify (a) x = t cos t , y = t sin t , z = 5 (b) x 2 + y 2 = z 2 2. (6) Write an equation in the indicated coordinate system. Also write a parametric equation and a vector equation for each of the following equation. (i) x 2 + y 2 = 25 in R 3 ; cylindrical coordinates, spherical coordinates (ii) x 2 + y 2 = 100 in R 2 ; polar coordinates 3. (3) x = t cos t , y = t sin t is a parametric equation of a curve in R 2 . Write a polar equation