For the following exercises, use a CAS and the divergence theorem to compute the net outward flux for the vector fields across the boundary of the given regions D . 415. Compute the flux of water through parabolic cylinder S : y = x 2 , from 0 ≤ x ≤ 2 , 0 ≤ z ≤ 3 , if the velocity vector is F ( x , y , z ) = 3 z 2 i + 6 j + 6 x z k .
For the following exercises, use a CAS and the divergence theorem to compute the net outward flux for the vector fields across the boundary of the given regions D . 415. Compute the flux of water through parabolic cylinder S : y = x 2 , from 0 ≤ x ≤ 2 , 0 ≤ z ≤ 3 , if the velocity vector is F ( x , y , z ) = 3 z 2 i + 6 j + 6 x z k .
For the following exercises, use a CAS and the divergence theorem to compute the net outward flux for the vector fields across the boundary of the given regions D.
415. Compute the flux of water through parabolic cylinder
S
:
y
=
x
2
, from
0
≤
x
≤
2
,
0
≤
z
≤
3
, if the velocity vector is
F
(
x
,
y
,
z
)
=
3
z
2
i
+
6
j
+
6
x
z
k
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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