MATH 0180 Midterm: MATH 180 Brown Exam m180s11a

• School: Brown University
• Department: Mathematics
• Course: MATH 0180
• Professor: All

Document Summary

Math 180 solution to quiz #11a: cole. Let s be the surface {(x, y, z) : x2 +y2 +z3 = 9, 1 z 2} with unit normal vector n pointing away from the z-axis. Solution: (a) g = xzez 0, y(2z) yzez, 0 z2 = xzez, 2yz yzez, z2 . (b) the boundary curves occur when z = 2 and z = 1. When z = 2, we have the circle c1: x2 +y2 = 9 z3 = 1. When z = 1, we have the circle c2: x2 +y2 = 9 z3 = 10. (c) we use stokes" theorem. So, i = i1 + i2 where i1 = c1. F dr. sin2 t dt = 4 . We parameterize c1 with r(t) = cos t, sin t, 2 for 0 t 2 . Since the direction is wrong, set c = 1.