Problem #4:Use the divergence theorem to find the outward fluxF.n dSof the vector fieldcos(3y + 4z) i + 2 In(x² + 6z) j + 4z² k, where S is the surface of the region bounded withinby the graphs of zFV64 – x2 – y² , x² + y²2, and z = 0.

Answered: Image /qna-images/answer/951f151a-cad9-48c7-814e-4f1f57397fe1.jpg

Answered: plem #4: Use the divergence theorem to…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.FOM: Focus On Modeling: Vectors Fields

Problem 18P

See similar textbooks

Similar questions

1) Consider the conservative vector field given by: F(x, y) = (exy3 + 2e2xy, e2x + 3exy2) A potential function that generates the vector field F corresponds to: A) f(x, y) = exy + exy3 B) f(x, y) = 3exy2 +(e2x/2)+(exy4)/4 C) f(x, y) = e2xy + exy3 D) f(x, y) = exy + e2xy3 2) Consider the vector field F(x, y, z) = (y - z sinx, x, 2z + cosx). The work that performs the F field to displace a body, from point A (3π, −1, 1) to point B (π, 2, 0) corresponds approximately to: A) 28, 45 JB) 32, 42 JC) 15, 71 JD) 13, 72 J
calc 3 13.7 #5 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 kS is the part of the paraboloid z = 2 − x2 − y2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, and has upward orientation.
Use the divergence theorem to find the outward flux ∫ ∫ S F · n dS of the vector field F = cos(5y + 10z) i + 5 ln(x2 + 3z) j + 4z2 k, where S is the surface of the region bounded within by the graphs of z = √ 49 − x2 − y2 , x2 + y2 = 10, and z = 0.
5. Find a potential function corresponding to the vector field F(x, y, z) = (2x, 3Y, 4z).
calc 3 13.9 #4 Use the Divergence Theorem to calculate the surface integral ∫∫S F · dS; that is, calculate the flux of F across S. F(x,y,z) = x2z3 i + 5xyz3 j + xz4 kS is the surface of the box with vertices (±2,±3,±1)
A conservative vector field is given by: F = (-z - 1)i + (-2y + 2)j + (-x - 1)k What 2 options give a potential function to F. A. U (x,y,z) = xz + x + y2 - 2y + z B. U (x,y,z) = 2xz + x + y2 - 2y + z C. U (x,y,z) = (x + 1) (z + 1) + (y - 1)2 D. U (x,y,z) = -x (-z - 1) + y2 - 2y - z (-x - 1) E. U (x,y,z) = x + 2y + z

Recommended textbooks for you

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

plem #4: Use the divergence theorem to find the outward flux || F.n dS of the vector field F = cos(3y + 4z) i + 2 In(x2 + 6z) j + 4z2 k, where S is the surface of the region bounded within by the graphs of z = V64 – x² – y² , x2 +y? = 2, and z = 0.