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Work In Exercises 37-42, find the work done by the force field F on a particle moving along the given path.
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Chapter 15 Solutions
Multivariable Calculus
- Showing Linear Independence In Exercises 27-30, show that the set of solutions of a second-order linear homogeneous differential equation is linearly independent. {eax,xeax}arrow_forwardFind the flux of the field F =(x + y)i -(x2+y2)j outward across the triangle with vertices (1, 0), (0, 1), (-1, 0).arrow_forwarduse Green’s Theorem to find the counterclock-wise circulation and outward flux for the field F and curve C. F = (x2 + 4y)i + (x + y2 )j C: The square bounded by x = 0, x = 1, y = 0, y = 1arrow_forward
- use Green’s Theorem to find the counterclock-wise circulation and outward flux for the field F and curve C. F = (y2 - x2 )i + (x2 + y2 )j C: The triangle bounded by y = 0, x = 3, and y =x.arrow_forwarduse Green’s Theorem to find the counterclock-wise circulation and outward flux for the field F and curve C. F = (x + y)i - (x2 + y2 )j C: The triangle bounded by y = 0, x = 1, and y = xarrow_forwardRain on a roof Consider the vertical vector field F = ⟨0, 0, -1⟩, correspondingto a constant downward flow. Find the flux in the downward direction acrossthe surface S, which is the plane z = 4 - 2x - y in the first octant.arrow_forward
- check the stokes theorem for vactor field A=(x)i+(y)j+(2xy)k where S is the lower hemisphere x2+y2+z2=4 and z<=0arrow_forwardFind the flux of the vector field F across the surface S in the indicated direction.F = x 2y i - z k; S is portion of the cone z = 4 square root of x^2+y^2 between z = 0 and z = 1; direction is outward a)-1/24pi b)-1/8pi c)1/24pi d)-1/48piarrow_forwardFind the flux of the field F = x i + y j + z k across the sphere x2 + y2 + z2 = a2 in the direction away from the origin.arrow_forward
- Find the flux of the vector field F across the surface S in the indicated direction.F = x 2y i - z k; S is portion of the cone z = 4 square root of x^2+y^2 between z = 0 and z = 1; direction is outward a)-1/24 pi b)-1/8 pi c)1/24 pi d)-1/48 piarrow_forwardUsing Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.F = xy i + x j; C is the triangle with vertices at (0, 0), (7, 0), and (0, 4)arrow_forwardFind the flux of the field F(x, y, z) = z2 i + x j - 3 z k outward through the surface cut from the parabolic cylinder z = 4 - y2 by the planes x = 0, x = 1, and z = 0.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning