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Use the Divergence Theorem to find the flux of F across the surface
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EBK CALCULUS EARLY TRANSCENDENTALS SING
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- Find the flux of F= ²7 + x³z³7 + 3xzk out of the closed region bounded by the planes z = 0, y = 0, x = y, x = 4, z = 5. Give the exact answer or round to three decimal places. The flux of F out of the closed region isarrow_forwardThe gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0). Select one: O True O Falsearrow_forwardEvaluate the circulation of G = xyi + zj + 4yk around a square of side 4, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Jo F. dr =arrow_forward
- Evaluate 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_forwardLet F(x, y, z) = xzi+yzj + xyk, Surface S is the part of the sphere x² + y² + z² = 4 that lies inside the cylinder x² + y² = 1 and above the xy-plane. Find a vector equation of the boundary curve C. (b) Compute for FdR (c) Compute for C F.Tdsarrow_forwardConsider the space curve represented by the intersection of the surfaces. Represent the curve by a vector-valued function r(t) using the given parameter. r(t) = Surfaces z = x² + 2y², x+y=0 Parameter x = tarrow_forward
- 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.arrow_forwardFind the centroidarrow_forwardUse Divergence theorem to find the outward flux of F = (7x², e¹², cos³x² + x)) OS of the cube in R³ bounded by the planes x = 0, x = 2, y = 0, y = 2, z = 0, z = 2.arrow_forward
- Identify the surface by eliminating the parameters from the vector-valued function r(u,v) = 3 cosv cosui + 3 cosv sinuj + Śsinvk a. plane b. sphere c. paraboloid d. cylinder e. ellipsoid d b a e (Darrow_forwardLet 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=arrow_forwardIntegrate g(x, y, z) = x + y + z over the portion of the plane 2x + 2y + z = 2 that lies in the first octant.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
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