Name: ID Number:TA: Section Time:MTH 234Exam 4: PracticeDecember 7, 201050 minutesSects: 16.1-16.5,16.7, 16.8.No calculators or any other devices allowed.If any question is not clear, ask for clarification.No credit will be given for illegible solutions.If you present different answers for the same problem,the worst answer will be graded.Show a ll your work.Box your answers.1. (20 points) Find the potential function for F =D2xy,(1 − x2)y2E, for y > 0.2. (20 points) Use the Green Theorem in the plane to show that line integral given byICxy2dx + (x2y + 2x) dy around any square depends only on the area of the squareand not on its location in the plane.3. (20 points) Write an integral which gives the surface area of the s urface cut from thehemisphere x2+ y2+ z2= 6, with z > 0 by the cylinder (x − 1)2+ y2= 1. Your finalanswer should be written in cylindrical coordinates. Do not evaluate the integral.4. (20 points) Use the Stokes Theorem to compute the line integral of the vector fieldF = hx2y, 1, zi along the path C given by the intersection of the cylinder x2+ y2= 4and the hemisphere x2+ y2+ z2= 16, with z > 0, counterclockwise when viewed fromabove.5. (20 points) Use the Divergence Theorem to find the outward flux of the field F =px2+ y2+ z2hx, y, zi across the boundary of the region D = {1 6 x2+ y2+ z26 2}.# Pts Score1 202 203 204 205 20Σ
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