Let F( x , y , z ) = 6 a + 1 x i − 4 a y j+ a 2 z k and let σ be the sphere of a radius a centered at the origin and oriented outward. Use a CAS to find all values of a such that flux of F across σ is zero.
Let F( x , y , z ) = 6 a + 1 x i − 4 a y j+ a 2 z k and let σ be the sphere of a radius a centered at the origin and oriented outward. Use a CAS to find all values of a such that flux of F across σ is zero.
Let
F(
x
,
y
,
z
)
=
6
a
+
1
x
i
−
4
a
y
j+
a
2
z
k
and let
σ
be the sphere of a radius a centered at the origin and oriented outward. Use a CAS to find all values of a such that flux of F across
σ
is zero.
Suppose is a constant vector. Let F(x, y, z) = C find the flux of F through a surface
S on plane with nonzero vectors A, B. In particular, the surface S is parametrized by
Flu, 0) = rõ tuổ+ vB for (u,v) er.
Let F(x, y) = 2x
2yi + 3xyj, and C be the boundary of the square with corner points (±1, ±1), positively oriented.
Find the flux of F
across C.
Consider the following function.
T: R2 → R, T(x, y) = (2x2, 3xy, y?)
Find the following images for vectors u =
(u,, u2) and v = (v,, v2) in R2 and the scalar c. (Give all answers in terms of
1'
"1, U2, V1, V2, and c.)
T(u)
T(v)
T(u) + T(v) =
T(u + v)
CT(u) =
T(cu) =
Determine whether the function is a linear transformation.
O linear transformation
not a linear transformation
Chapter 15 Solutions
Calculus Early Transcendentals, Binder Ready Version
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