Math 2300 FS2015-In order to receive full credit, show all of your work

| August 30, 2017

Question
Math 2300 FS2015, Dr. Hesam Oveys
Quizzes 10, 11, & 12, DUE: Wednesday, December 9, 2015
Name:
Student Number:
In order to receive full credit, show all of your work in a clear, logical manner.
Write your solutions on this sheet (and back) or attach pages as necessary.
1. (6 points) Let the surface S be the portion of the paraboloid z = x2 +y 2 inside the cylinder x2 +y 2 = 4.
¨
1 dS.

Compute area(S) =
S

¨
2. (6 points) Compute

x + y dS, where S is the portion of the plane z = 4x + y above the region
S

bounded by y = x2 and y = 1 on the xy-plane.
¨
F · dS, where F(x, y, z) = −x, −y, z 3 , and S is the portion of the cone
3. (6 points) Compute
S

x2 + y 2 between the planes z = 1 and z = 3 (use the downward pointing normal).
ˆ
4. (6 points) Use Stokes’ Theorem to compute
F · dr, where F(x, y, z) = xy, 2z, 3y , and C is the
z=

C

curve of intersection of the plane x + z = 5 and the cylinder x2 + y 2 = 9.
¨
5. (6 points) Use the Divergence Theorem to compute
F·dS, where F(x, y, z) = x3 +y 3 , y 3 +z 3 , z 3 +
S

x3 , and S is the sphere centered at the origin with radius 2 (use the outward pointing normal).

1

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