The Divergence Theorem Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Verify the divergence theorem for the vector function and ball given by where is the unit normal vector pointing away from the origin.

(2) Verify the divergence theorem for the vector function and tetrahedron bounded by the coordinate planes and

(3) Use the divergence theorem to evaluate the surface integral for the vector function and closed boundary surface given by the hemisphere together with the disk in the -plane, where is the unit normal vector pointing away from the origin.

(4) Use the divergence theorem to evaluate the surface integral for the vector function and closed boundary surface given by the five faces of the unit cube, and missing and where is the unit normal vector pointing away from the origin.

(5) Use the divergence theorem to evaluate the surface integral for the vector function and closed boundary surface given by the sphere

(6) Use the divergence theorem to evaluate the surface integral for the vector function and closed boundary surface given by the solid bounded by the cylinder and the planes and

(7) Use the divergence theorem to evaluate the surface integral for the vector function and closed boundary surface given by the solid bounded above by the sphere and below by the cone in spherical coordinates.

(8) Use the divergence theorem to evaluate where and is the sphere with constant

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The Divergence Theorem Homework
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/the-divergence-theorem-homework.html