Question
In: Math
verify Stokes' thm.Assume that the surface S is oriented upward F = 2zi - 3xj +...
verify Stokes' thm.Assume that the surface S is oriented upward F = 2zi - 3xj + 4yk ; S that portion of the paraboloid z =16 - x2- y2 for z>=0. My primary is how to convert dS into dA
Solutions
milcah answered 2 years agoRelated Solutions
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed...
Use Stokes' Theorem to evaluate
C
F · dr
where C is oriented counterclockwise as viewed from
above.
F(x, y,
z) = (x +
y2)i +
(y +
z2)j +
(z +
x2)k,
C is the triangle with vertices
(7, 0, 0), (0, 7, 0), and (0, 0, 7).
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed...
Use Stokes' Theorem to evaluate C F · dr where C is oriented
counterclockwise as viewed from above. F(x, y, z) = xyi + 3zj +
7yk, C is the curve of intersection of the plane x + z = 10 and the
cylinder x2 + y2 = 9.
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed...
Use Stokes' Theorem to evaluate C F · dr where C is oriented
counterclockwise as viewed from above. F(x, y, z) = xyi + 3zj +
5yk, C is the curve of intersection of the plane x + z = 2 and the
cylinder x^2 + y^2 = 144.
1A) Let S be the upward oriented surface of the box [-pi,pi]x[0,pi]x[0,pi]without the face xy plane....
1A) Let S be the upward oriented surface of the
box [-pi,pi]x[0,pi]x[0,pi]without the face xy plane. That is, in
the standard view, the box has a front and back, a left and right
face, a top face, but no bottom face. Let
F(x,y,z)=< ycos(z),zcos(x),xcos(y) >. Find
the flux of curl F across S directly, without
using stokes theorem.
1B) Let S be the upward oriented
surface of the box [-pi,pi]x[0,pi]x[0,pi]without the face xy plane.
That is, in the standard view, the box...
Evaluate the surface integral S F · dS for the given vector field F and the...
Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S. In other words, find the flux of
F across S. For closed surfaces, use the
positive (outward) orientation.
F(x, y, z) = xy i + yz j + zx k
S is the part of the paraboloid
z = 6 − x2 − y2 that lies above the square
0 ≤ x ≤ 1, 0 ≤ y ≤ 1,
and has...
Evaluate the surface integral S F · dS for the given vector field F and...
Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S. In other words, find the flux of
F across S. For closed surfaces, use the
positive (outward) orientation.
F(x, y, z) = x i − z j + y k
S is the part of the sphere
x2 + y2 + z2 = 1
in the first octant, with orientation toward the origin
Evaluate the surface integral S F · dS for the given vector field F and...
Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S. In other words, find the flux of
F across S. For closed surfaces, use the
positive (outward) orientation.
F(x, y, z) = x i − z j + y k
S is the part of the sphere
x2 + y2 + z2 = 9
in the first octant, with orientation toward the origin
Evaluate the surface integral S F · dS for the given vector field F and the...
Evaluate the surface integral
S
F ·
dS for the given
vector field F and the oriented surface
S. In other words, find the flux of F
across S. For closed surfaces, use the positive (outward)
orientation.
F(x, y, z) =
xzey i −
xzey j + z
k
S is the part of the plane x + y +
z = 3 in the first octant and has downward orientation
Evaluate the surface integral S F · dS for the given vector field F and...
Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S. In other words, find the flux of
F across S. For closed surfaces, use the
positive (outward) orientation.
F(x, y, z) = x i + y j + z4 k
S is the part of the cone z =
x2 + y2
beneath the plane
z = 1
with downward orientation
For the function f(x)=x4-4x3 , find the following: local minima and/or maxima (verify) inflection point(s) (verify)
For the function f(x)=x4-4x3 , find the
following:
local minima and/or maxima (verify)
inflection point(s) (verify)
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