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

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

∇f · dr along the given curve C.

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related 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

Consider the following function: f (x , y , z ) = x 2 + y...

Consider the following function: f (x , y , z ) = x 2 + y 2 + z 2 − x y − y z + x + z (a) This function has one critical point. Find it. (b) Compute the Hessian of f , and use it to determine whether the critical point is a local man, local min, or neither? (c) Is the critical point a global max, global min, or neither? Justify your answer.

Subjects