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 . 419. Evaluate ∬ s F ⋅ d S , where F ( x , y , z ) = b x y 2 i + b x 2 y j + ( x 2 + y 2 ) z 2 k and S is a closed surface bounding the region and consisting of solid cylinder x 2 + y 2 ≤ a 2 and 0 ≤ z ≤ b .
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 . 419. Evaluate ∬ s F ⋅ d S , where F ( x , y , z ) = b x y 2 i + b x 2 y j + ( x 2 + y 2 ) z 2 k and S is a closed surface bounding the region and consisting of solid cylinder x 2 + y 2 ≤ a 2 and 0 ≤ z ≤ b .
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.
419. Evaluate
∬
s
F
⋅
d
S
, where
F
(
x
,
y
,
z
)
=
b
x
y
2
i
+
b
x
2
y
j
+
(
x
2
+
y
2
)
z
2
k
and S is a closed surface bounding the region and consisting of solid cylinder
x
2
+
y
2
≤
a
2
and
0
≤
z
≤
b
.
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.
Mathematics for Elementary Teachers with Activities (5th Edition)
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