MATH 241 Midterm: MATH 241 UIUC Math241_Fall08_2PM_Exam4

• School: University of Illinois
• Department: Mathematics
• Course: MATH 241
• Professor: All

Document Summary

Math 241 exam 4 2pm v1. 2. (a) (5pts) compute zc y dx x dy x2 + y2 oriented counterclockwise. 3. (a) (4pts) let s be the sphere x2 + y2 + z 2 = 16. S is the portion of the paraboloid z = 4 x2 y2 above the xy-plane, oriented so that the unit nomral vectors point to the outside of the paraboloid. Math 241 exam 4 2pm v2. Y dx + x dy x2 + y2 oriented counterclockwise. 3. (a) (4pts) let s be the sphere x2 + y2 + z 2 = 4. Compute the ux of the vector eld f across the surface s. 5. (a) (4pts) state the formula at the conclusion of stokes" theorem. (b) (7pts) evaluate zzs ( f ) n ds, where f (x, y, z) = (ez2. , 4x y, 8z sin y) and where.