Use the Divergence Theorem to find the flux of F across the surface
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
Calculus: Early Transcendentals, Enhanced Etext
Additional Math Textbook Solutions
Calculus: Early Transcendentals (3rd Edition)
Precalculus: Mathematics for Calculus (Standalone Book)
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Precalculus Enhanced with Graphing Utilities (7th Edition)
Calculus & Its Applications (14th Edition)
- find the outward flux of F across the boundary of D. F =-2x i - 3y j + z k D: The upper region cut from the solid sphere x2 + y2 + z2 <=2 by the paraboloid z = x2 + y2arrow_forwardFind the flux of F= (y, z-y, z) across the tetrahedron with vertices (0,0,0), (1,0,0), (0, 1,0), (0,0,1) and has the outward orientation.arrow_forwardFind the flow of F=xzi-yk through the upper part of plane z-1 in the x + y +2 = 4sphere.arrow_forward
- Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x2 + xy + 1.arrow_forwardLet F(x, y, z)=(v)i+(x)j+(z²)k. Find the flux of F across the positively oriented closed surface S where S is the surface of the sphere x + y +z² = 4.arrow_forwardConsider a surface defined by F(x, Y, z) = 0 whose gradient is (cos(r2), z² e", 2ze"). The equation of the tangent plane to the surface at the point (-2,0, 1) is O x + y+ 2z -1 = 0 x - y – 2z + 4 = 0 x – z + 3 = 0 O x + y + 2z = 0arrow_forward
- Evaluate F.ndS for the given F and ơ. (b) F(x, y, z) = (x² + y) i+ xyj – (2xz + y) k, o : the surface of the plane x + y + z = 1 in the first octantarrow_forwardThe vector v = <a, 1, -1>, is tangent to the surface x2 + 2y3 - 3z2 = 3 at the point (2, 1, 1). Find a.arrow_forward→>> Let S be the surface in R³ that is the image of the function F: R² R³ given by F(u, v) = (u², v²,u+v). Let R be the surface in R³ given by 2x² + y² +2²= 7. Observe that the surfaces both contain the point (1, 1,2). Find the parametric equation of the line that is tangent to both surfaces at that point.arrow_forward
- Let F(x, y, z) Find an equation for the tangent plane to the level surface F(x, y, z) in R³) at the point (xo, Yo, 2o) = (1,0, 0). 8x2 + 2y2 + 4z², which represents a three-dimensional surface in R4. 8 (an ellipsoidarrow_forwardLet 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.arrow_forwardEvaluate the circulation of G = xyi+zj+7yk around a square of side 9, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Prevs So F.dr-arrow_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