Given the following vector force field, F, is
conservative:
F(x,y)=(2x2y4+x)i+(2x4y3+y)j,
determine the work done subject to...
Given the following vector force field, F, is
conservative:
F(x,y)=(2x2y4+x)i+(2x4y3+y)j,
determine the work done subject to the force while traveling along
any piecewise smooth curve from (-2,1) to (-1,0)
A velocity vector field is given by F (x, y) = - i + xj
a) Draw this vector field.
b) Find parametric equations that describe the current lines in
this field. c)
Obtain the current line which passes through point (2,0) at time
t = 0 and represent it graphically. d)
Obtain the representation y = f(x) of the current line in part
c).
The flow of a vector field is F=(x-y)i+(x^2-y)j along the
straight line C from the origin to the point (3/5, -4/5)
A. Express the flow described above as a single variable
integral.
B. Then compute the flow using the expression found in part
A.
Please show all work.
Find the flux of the vector field F =
x i +
e2x j +
z k through the surface S given
by that portion of the plane 2x + y +
8z = 7 in the first octant, oriented upward.
Questions Determine whether or not the vector field is
conservative. If it is conservative, find a vector f f such that .
F→=∇f. → F ( x , y , z ) =< y cos x y, x cos x y , − sin z >
F→ conservative. A potential function for → F F→ is f ( x , y , z )
= f(x,y,z)= + K. (Type "DNE" if → F F→ is not conservative.)
The Vector Field f(x, y) = (2x + 2y^2)i + (4xy - 6y^2)j has
exactly one potential function f (x, y) that satisfies f(0, 0).
Find this potential function , then find the value of this
potential function at the point (1, 1).
Find the work done by the force field F(x,y) =
<2xy-cosx,ln(xy)+cosy> along the path C, where C starts at
(1,1)(1,1) and travels to (2,4)(2,4) along y=x^2, then travels down
to (2,2)(2,2) along a straight path, and returns to (1,1)(1,1)
along a straight path. Fully justify your solution.
Verify the Divergence Theorem for the vector field F(x, y, z) =
< y, x , z^2 > on the region E bounded by the planes y + z =
2, z = 0 and the cylinder x^2 + y^2 = 1.
By Surface Integral:
By Triple Integral:
Find the work done by the vector vield
F(x, y)
=
3x+3x2y,
3y2x+2x3
on a particle moving first from
(−3, 0),
along the x-axis to (3, 0), and then returning
along
y =
9 −
x2
back to the starting point.