Question
In: Math
Consider F and C below. F(x, y, z) = 2xz + y2 i + 2xy j...
Consider F and C below.
F(x, y, z) =
2xz + y2
i + 2xy j +
x2 + 15z2
k
C: x = t2, y = t + 2, z = 4t − 1, 0 ≤ t ≤ 1
(a) Find a function f such that F = ∇f.
f(x, y, z) =
(b) Use part (a) to evaluate
| C |
∇f · dr along the given curve C.
Solutions
milcah answered 2 years agoRelated Solutions
Consider F and C below. F(x, y, z) = 2xz + y2 i + 2xy j...
Consider F and C below.
F(x, y, z) =
2xz + y2
i + 2xy j +
x2 + 6z2
k
C: x = t2, y = t +
2, z = 3t − 1, 0 ≤ t
≤ 1
(a) Find a function f such that F =
∇f.
f(x, y, z) =
x2z+xy2+2z3+c
(b) Use part (a) to evaluate
C
∇f · dr along the given curve C.
Consider F and C below. F(x, y, z) = yz i + xz j + (xy...
Consider F and C below.
F(x, y, z) = yz i + xz j + (xy + 14z) k
C is the line segment from (3, 0, −1) to (6, 4, 2)
(a) Find a function f such that F =
∇f.
f(x, y, z) =
(b) Use part (a) to evaluate
C
∇f · dr along the given curve C.
Consider F and C below. F(x, y, z) = yz i + xz j + (xy...
Consider F and C below.
F(x, y, z) = yz i + xz j + (xy + 14z) k
C is the line segment from (3, 0, −3) to (5, 5, 1)
(a) Find a function f such that F =
∇f.
f(x, y, z) =
(b) Use part (a) to evaluate
C
∇f · dr along the given curve C.
Let F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 8)j + zk. Find the...
Let
F(x, y,
z) = z
tan−1(y2)i
+ z3
ln(x2 + 8)j +
zk.
Find the flux of F across S, the part
of the paraboloid
x2 +
y2 + z = 28
that lies above the plane
z = 3
and is oriented upward.
S
F · dS =
Let F (x, y) = y sin x i – cos x j, where C is...
Let F (x, y) = y sin x i – cos x j, where C is the line segment
from (π/2,0) to (π, 1). Then C F•dr is
A 1
B 2
C 5/2
D 3
E 7/2
Evaluate the line integral ∫_C F⋅dr, where F(x,y,z)=−4sin(x)i+3cos(y)j−4xzk and C is given by the vector function...
Evaluate the line integral ∫_C F⋅dr, where
F(x,y,z)=−4sin(x)i+3cos(y)j−4xzk and C is given by the vector
function r(t)=t^6i−t^5j+t^4k , 0≤t≤1.
Let F(x, y, z) = z tan^−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find the...
Let F(x, y, z) = z tan^−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find
the flux of F across S, the part of the paraboloid x2 + y2 + z = 29
that lies above the plane z = 4 and is oriented upward.
Let F= (x2 + y + 2 + z2) i + (exp( x2 ) + y2) j...
Let F= (x2 +
y + 2 + z2) i + (exp(
x2 ) + y2)
j + (3 + x) k . Let a
> 0 and let S be part of the spherical
surface x2 + y2 +
z2 = 2az + 15a2
that is above the x-y plane and the disk formed in the
x-y plane by the circular intersection between the sphere
and the plane. Find the flux of F outward across
S.
Verify Stokes theorem for F =(y^2 + x^2 - x^2)i + (z^2 + x^2 - y^2)j...
Verify Stokes theorem for F =(y^2 + x^2 - x^2)i + (z^2 + x^2 -
y^2)j + (x^2 + y^2 - z^2)k over the portion of the surface x^2 +
y^2 -2ax + az = 0
The curried version of let f (x,y,z) = (x,(y,z)) is let f (x,(y,z)) = (x,(y,z)) Just...
The curried version of let f (x,y,z) = (x,(y,z)) is
let f (x,(y,z)) = (x,(y,z))
Just f (because f is already curried)
let f x y z = (x,(y,z))
let f x y z = x (y z)
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