Using the Divergence Theorem In Exercises 9-18, use the Divergence Theorem to evaluate
and find the outward flux of F through the surface of the solid S bounded by the graphs of the equations. Use a computer algebra system to verify your results.
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
Multivariable Calculus
- Computing flux Use the Divergence Theorem to compute thenet outward flux of the following fields across the given surface S. F = ⟨x, y, z⟩; S is the surface of the paraboloidz = 4 - x2 - y2, for z ≥ 0, plus its base in the xy-plane.arrow_forwardUsing Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.F = (x 2 + y 2) i + (x - y) j; C is the rectangle with vertices at (0, 0), (6, 0), (6, 9), and (0, 9) a)540 b)432 c)0 d)-432arrow_forwardComputing flux Use the Divergence Theorem to compute thenet outward flux of the following fields across the given surface S. F = ⟨x, 2y, z⟩; S is the boundary of the tetrahedron in the firstoctant formed by the plane x + y + z = 1.arrow_forward
- Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.F = (x - y) i + (x + y) j; C is the triangle with vertices at (0, 0), (7, 0), and (0, 6) a) 0 b) 252 c) 84 d) 42arrow_forwardUsing the divergence theorem, find the outward flux of F across the boundary of region D. F=zi+xyj+zyk; D: the solid cube cut by the coordinate planes and the planes x=4, y=4, x=4.arrow_forwardUsing Gauss' theorem to calculate the flow of the vector field 3x3 F: F (x, y, z) = (x^2z, 2x^2, 3z^2) exiting the cylinder defined from the relations x ^2+y ^2<=1, 1<= z <= 2.arrow_forward
- Computing flux Use the Divergence Theorem to compute thenet outward flux of the following fields across the given surface S. F = ⟨x, -2y, 3z⟩; S is the sphere {(x, y, z): x2 + y2 + z2 = 6}.arrow_forwardUse Green's Theorem to find the counterclockwise circulation of F around the closed curve C. F=(x²+y²)i+(x-y)j; C is the rectangle with vertices at (0,0), (2,0), (2,2), (0,2)arrow_forwardse the Divergence Theorem to evaluate S F · N dS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results. F(x, y, z) = x3i + x2yj + x2eyk S: z = 4 − y, z = 0, x = 0, x = 3, y = 0arrow_forward
- Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. F= xyi+ xj; C is the triangle with vertices at (0,0), (10,0), and (0,2)arrow_forwardUsing Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.F = (3x + 3y) i + (4x - 9y) j; C is the region bounded above by y = -2x 2 + 45 and below by y=3x2 in the first quadrant. answers a)90 b)- 294 c)-132 d)252arrow_forwardUsing the Divergence Theorem, find the outward flux of F across the boundary of the region D.F = z i + xy j + zy k; D: the solid cube cut by the coordinate planes and the planes x=1, y = 1, and z = 1arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning