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 . 422. [T] Use a CAS and the divergence theorem to evaluate ∬ s F ⋅ d S , Where F ( x , y , z ) = ( 2 x + y cos z ) i + ( x 2 − y ) j + y 2 z k and S is sphere x 2 + y 2 + z 2 = 4 orientated outward.
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 . 422. [T] Use a CAS and the divergence theorem to evaluate ∬ s F ⋅ d S , Where F ( x , y , z ) = ( 2 x + y cos z ) i + ( x 2 − y ) j + y 2 z k and S is sphere x 2 + y 2 + z 2 = 4 orientated outward.
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.
422. [T] Use a CAS and the divergence theorem to evaluate
∬
s
F
⋅
d
S
, Where
F
(
x
,
y
,
z
)
=
(
2
x
+
y
cos
z
)
i
+
(
x
2
−
y
)
j
+
y
2
z
k
and S is sphere
x
2
+
y
2
+
z
2
=
4
orientated outward.
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.
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