For the following exercises, use a computer algebraic system (CAS) and the divergence theorem to evaluate surface integral ∫ s F ⋅ n d S for the given choice of F and the boundary surface S . For each closed surface, assume N is the outward unit normal vector . 388. Use the divergence theorem to calculate surface integral ∬ s F ⋅ d S when F ( x , y , z ) = z tan − 1 ( y 2 ) i + z 3 I n ( x 2 + 1 ) j + z k and S is a part of paraboloid x 2 + y 2 + z = 2 that lies above plane z = 1 and is oriented upward.
For the following exercises, use a computer algebraic system (CAS) and the divergence theorem to evaluate surface integral ∫ s F ⋅ n d S for the given choice of F and the boundary surface S . For each closed surface, assume N is the outward unit normal vector . 388. Use the divergence theorem to calculate surface integral ∬ s F ⋅ d S when F ( x , y , z ) = z tan − 1 ( y 2 ) i + z 3 I n ( x 2 + 1 ) j + z k and S is a part of paraboloid x 2 + y 2 + z = 2 that lies above plane z = 1 and is oriented upward.
For the following exercises, use a computer algebraic system (CAS) and the divergence theorem to evaluate surface integral
∫
s
F
⋅
n
d
S
for the given choice of F and the boundary surface S. For each closed surface, assume N is the outward unit normal vector.
388. Use the divergence theorem to calculate surface integral
∬
s
F
⋅
d
S
when
F
(
x
,
y
,
z
)
=
z
tan
−
1
(
y
2
)
i
+
z
3
I
n
(
x
2
+
1
)
j
+
z
k
and S is a part of paraboloid
x
2
+
y
2
+
z
=
2
that lies above plane
z
=
1
and is oriented upward.
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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