Show all steps. Correct answer is : 3.1415926535898 -- -| Let v = (x²z, 1 — 2xyz - 3y+ x²y, 3z − x²z) be the velocity field of a fluid. Compute the flux ofacross the surface x² + y² + z² = 1 where y > 0 and the surface is oriented away from the origin.Hint: Use the Divergence Theorem.ʊ

Answered: - - - | Let v = (x²z, 1 — 2xyz - 3y+…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

Use fundamental theorem of calculus
Let F = -9zi+ (xe#z– 2xe**)}+ 12 k. Find f, F·dĀ, and let S be the portion of the plane 2x + 3z = 6 that lies in the first octant such that 0 < y< 4 (see figure to the right), oriented upward. Z Explain why the formula F · A cannot be used to find the flux of F through the surface S. Please be specific and use a complete sentence.
Let v = (xʻz, 3 – 4xyz, xz“) be the velocity field of a fluid. Compute the flux of v across the surface 16x? + 9z? (y – 12) where 0 < y < 12 and the surface is oriented away from the origin.
F21.
Calculate the flux of the vector field F(x, y, z) = (3x + 5)2 through a disk of radius 4 centered at the origin in the yz-plane, oriented in the negative x-direction. Flux: =
a) What is the flux of the constant vector field F = (a, b, c) through any closed surface? b) Is the flux of F = (x³, y³, z³) through any closed surface positive, negative, or zero?
Please don't provide handwritten solution .....
I only need part B,C, and D. Thank you.
Use Stokes Theorem
Let v = (x²z, 2 – 2xyz − 3y + x²y, 3z — x²z) be the velocity field of a fluid. Compute the flux of v across the surface x² + y² + z² = 9 where y > 0 and the surface is oriented away from the origin. Hint: Use the Divergence Theorem.
Let F = -9zi+ (xe"z – 2xe*)}+ 12 k. Find f, F•JÃ, and let S be the portion of the plane 2x + 3z = 6 that lies in the first octant such that 0 < y< 4 (see figure to the right), oriented upward. Can Stokes' Theorem be used to find the flux of F through S? Clearly answer yes or no, and then briefly explain your answer.
Let F(x, y) = (4x²,3y2). Compute the flux F nds of F across the boundary of the triangle with vertices (0,0), (2,0), (0, 2) • using the vector form of Green's Theorem. (Use symbolic notation and fractions where needed.) fr F.nds=

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

- - - | Let v = (x²z, 1 — 2xyz - 3y+ x²y, 3z − x²z) be the velocity field of a fluid. Compute the flux of across the surface x² + y² + z² = 1 where y > 0 and the surface is oriented away from the origin. Hint: Use the Divergence Theorem. ʊ