Find the flux of F across the surface σ by expressing σ parametrically. F( x , y , z ) = i + j + k ; the surface σ is the portion of the cone z = x 2 + y 2 between the planes z = 1 and z = 2 , oriented by downward unit normals.
Find the flux of F across the surface σ by expressing σ parametrically. F( x , y , z ) = i + j + k ; the surface σ is the portion of the cone z = x 2 + y 2 between the planes z = 1 and z = 2 , oriented by downward unit normals.
Find the flux of F across the surface
σ
by expressing
σ
parametrically.
F(
x
,
y
,
z
)
=
i
+
j
+
k
;
the surface
σ
is the portion of the cone
z
=
x
2
+
y
2
between the planes
z
=
1
and
z
=
2
,
oriented by downward unit normals.
Let C be the upper half of the circle whose equation is x? + (y - 2)2 = 1. Let S be the surface
that is generated by revolving curve C along the x-axis. Describe S using a vector function of 2
3 3V3
variables and find an equation of the plane tangent to the surface S at the point (0, ).
Consider the surface S given by the equation
f(r) = 2x − y³ +2²=0
(a) Confirm that the point P, with position p = (-1,-1, 1), lies on surface S and find a vector
normal to S at P.
(b) Find the equation of the plane tangent to S at P and the x-intercept of that plane.
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