F. dS; that is, calculate the flux of F across S. Js Use the divergence theorem to calculate the surface integral F(x, y z) = xe"i + (z - e")j - xy k, s is the ellipsoid x2 + 5y2 + 822 = 25
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How do I use the divergence theorem to calculate this?
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- Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x2 + xy + 1.a) Find a vector parametric equation for the ellipse that lies on the plane y - 4x + z = -8 and inside the cylinder y = 4. x2 + r(u, v) = for 0 < u < 2 and 0 < v < 2n. (6) aA = 7, x, = X. (c) dA = usqrt3 (d) Set up and evaluate a double integral for the surface area of the ellipse. Surface area =Evaluate Curlv•ñ, where v = 2xyi + (x² – 2y)j + xzk and i is a unit vector normal to the surface shown in the figure: (i) (ii) Z 1 surface z=1 surface y=1 1 1 1
- 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 = -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.Evaluate 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 =
- Find the linearization L(z, y) of f at the given point. Surface: f(r, y) 6tan '(ary) (2) Point: 2, Find exact values and no decimals. L(r, y)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 (DFind the flux of F across the surface σ by expressing σ parametrically. F(x,y,z)= 3i −7j+zk; σ is the portion of the cylinder x^2 +y^2 =16 between the planes z =−2 and z = 2, oriented by outward unit normals.
- Q3 Evaluate Curlv•ñ , where v = 2xyi +(x² –2 y)j +xzk and ñ is a unit vector normal to the surface shown in the figure: (1) surface z=i surface y=1 04Determine the flux of F(x, y, z) = < −x2 + x, y, 8x3 − z + 9 > across the surface with an upward orientation. Let the surface be the portion of the paraboloid z = 9 − 4x2 −4y2 on the first octant above the plane z = 1.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-