exam4-223

# exam4-223 - points(0 1 1(2 1 1 and(2 3 1 and oriented...

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Math 223-008 Exam # 4 Partial credit is possible, but you must show all work. Name: I hereby testify that this is individual work. Signed: 1. Use the divergence theorem (or your favorite method) to ﬁnd the ﬂux of -→ F = x 2 -→ i + y 2 -→ j + z 2 -→ k through the (open) surface S : z = 2 p x 2 + y 2 oriented upward with 0 z 4.

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2 2. Find the ﬂux of the vector ﬁeld -→ F = 1 x 2 + y 2 + z 2 ± 2 -→ i - 3 -→ j ² through a sphere of radius 2 centered at the origin.
3 3. (a) Find the curl of -→ F = ( z - 2 y ) -→ i + (3 x - 4 y ) -→ j + ( z + 3 y ) -→ k (b) Find the ﬂux of c url -→ F through the triangular plate bounded by the

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Unformatted text preview: points (0, 1, 1), (2, 1, 1) and (2, 3, 1), and oriented upwards. 4 4. (a) Find the ﬂux of-→ F = e z 2 cos z-→ i + x 3 e z 3-→ j + 4 z-→ k across the closed surface C bounded by the cylinder x 2 + y 2 = 25 and the planes z =-2 and z = 2. Assume the normal unit vector-→ n is outward on C . (b) Calculate the contributions to this ﬂux from the sides L 1 : z =-2, L 2 : z = 2 and from the (open) surface S : x 2 + y 2 = 25....
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exam4-223 - points(0 1 1(2 1 1 and(2 3 1 and oriented...

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