16.9 Homework - The Divergence Theorem (Homework)

1. [011 Points] DETAILS PREVIOUS ANSWERS SCALCET916.9.DDS. MY NOTES ASK YOUR TEACHER Use the divergence theorem to calculate the surface integral ff F - d5; that is, calculate the ux of F across 5. s F(X, y, z) = xyezi + xyzzaj 7 ye2 k, S is the surface of the box bounded by the coordinate planes and the planes x = 9, y = 2, and 2 = 1 X 2. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 16.9.007.MI. MY NOTES ASK YOUR TEACHER Use the divergence theorem to calculate the surface integral F . ds; that is, calculate the flux of F across S. F(x, y, z) = 3xy2i+ xe/j + z k, S is the surface of the solid bounded by the cylinder yz + zz = 9 and the planes x = -1 and x = 1 8T X Need Help? Read It Watch It Master It3. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 16.9.009. MY NOTES ASK YOUR TEACHER Use the divergence theorem to calculate the surface integral F . ds; that is, calculate the flux of F across S. F(x, y z) = xevi + (z - e))j - xyk, S is the ellipsoid x2 + 5y2 + 7z2 = 25 4.212 X Need Help? Read It4. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 16.9.013. MY NOTES ASK YOUR TEACHER Use the divergence theorem to calculate the surface integra F . dS; that is, calculate the flux of F across S. F(x, y z) = x2zi + xz j + y In(x + 1)k, S is the surface of the solid bounded by the planes x + 2z = 4, y = 6, x = 0 y = 0, and z = 0 x + 2z = 4 y = 6 X5. [011 Points] DETAILS PREVIOUS ANSWERS SCALCET916.9.IJ17. MY NOTES ASK YOU R TEACH ER Use the divergence theorem to calculate the surface integral ff F - d5; that is, calculate the ux of F across 5. s F = |r| r, where r = xi + yj + 2k, S consists of the hemisphere z = if 4 7 x2 7 y? and the disk x2 + y2 S 4 in the xyiplane 31.5 x Need Help? 7. [0.5/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 16.9.024. MY NOTES ASK YOUR TEACHER Plot the vector field and guess where div(F) > 0 and where div(F) 0 for y > -x; div(F) 0 for y -x O div(F) > 0 for y > x; div(F) 0 for y x Calculate div(F) to check your guess. div(F) = 2 X