For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 351. Let S be hemisphere x 2 + y 2 + z 2 = 4 with z ≥ 0 , oriented upward. Let F ( x , y , z ) = x 2 e y z i + y 2 e x z j + z 2 e x y k be a vector field. Use Stokes’ theorem to evaluate ∬ s c u r l F ⋅ d S .
For the following exercises, use Stokes’ theorem to evaluate ∬ s ( c u r l F ⋅ N ) d S for the vector fields and surface. 351. Let S be hemisphere x 2 + y 2 + z 2 = 4 with z ≥ 0 , oriented upward. Let F ( x , y , z ) = x 2 e y z i + y 2 e x z j + z 2 e x y k be a vector field. Use Stokes’ theorem to evaluate ∬ s c u r l F ⋅ d S .
For the following exercises, use Stokes’ theorem to evaluate
∬
s
(
c
u
r
l
F
⋅
N
)
d
S
for the vector fields and surface.
351. Let S be hemisphere
x
2
+
y
2
+
z
2
=
4
with
z
≥
0
, oriented upward. Let
F
(
x
,
y
,
z
)
=
x
2
e
y
z
i
+
y
2
e
x
z
j
+
z
2
e
x
y
k
be a vector field. Use Stokes’ theorem to evaluate
∬
s
c
u
r
l
F
⋅
d
S
.
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.
2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.
write it down for better understanding please
1. Suppose F(t) gives the temperature in degrees Fahrenheit t minutes after 1pm. With a
complete sentence, interpret the equation F(10) 68. (Remember this means explaining
the meaning of the equation without using any mathy vocabulary!) Include units. (3 points)
=
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.