Let S be the closed surface that bounds the region enclosed by the plane z = 4 and the circular paraboloid z = x² + y2, and let F(x, y, z)=-3xi - 3yj - 4zk. Verify the divergence theorem by calculating the outward flux of F through S, both as a surface integral and as a triple integral. Show all work clearly on your paper. No need to type anything here.

Q: Find the points on the sphere with center at the origin of radius 3 where the function f(x, y, z) =…

A:

Q: Determine the flux of F(x, y, z) = across the surface with an upward orientation. Let the surface…

A:

Q: Draw the parameterized surface

A:

Q: Find an equation for the tangent plane to the surface z = 6x3y2 + 3y at the point P(1, -3). Hint:…

A:

Q: Q1// Evaluate , F ds where F = yi + xj + 4zk and S is the surface x? + y? = 9 in the first octant…

A:

Q: Let z = g(x, y) = f(3 cos(ry), y + ev) provided that f(3, 6) = 4, fi(3, 6) = 2, f2(3, 6) = 3. %3D i)…

A:

Q: 2. Let S be the surface given by r(u, v) = (u, u² + v², v). Find the equation of the tangent plane…

A:

Q: b) Given F(.r, y. :) = (r + cosh 2)i+ (2y-3r*y)j-(r + 4y*:) k. Use Gauss's theorem to calculate F.n…

A:

Q: Let z = 9(x, y) = f(3 cos(xy), y + e™y) provided that f(3,7) = 4, fi (3, 7) = 2, f2(3, 7) = 3. i)…

A:

Q: Let F(x, y, z) Find an equation for the tangent plane to the level surface F(x, Y, z) = 8 (an…

A:

Q: tz = g(x, y) = f(3 cos(xy), y + e#") provided that f(3, 7) = 4, f1(3, 7) = 2, (3, 7) = 3. %3D Find…

A:

Q: F.N= (b) Calculate the normal component of F to the surface at P = (1, 2, 9) = (2, 3). (Use symbolic…

A: Given:It is given that  and  is the oriented surface parameterized by  for  and .To Find:(a) We have…

Q: Let z = g(x, y) = f(3 cos(ry), y + e) provided that f(3, 6) = 7, fi(3, 6) = 2, f2(3,6) = 3. i) Find…

A:

Q: b) Use Gauss theorem to evaluate F.ndS, where F(r, y, 2) = (2x²y² + In z) i – xy³ j – tanh(a² + y³)…

A:

Q: Let z = g(x, y) = f(3 cos(xy), y+ e#y) provided that f(3,6) = 6, f1(3, 6) = 2, f2(3, 6) = 5. i) Find…

A:

Q: c) Use Stokes' theorem to evaluate where F(x, y, z) = (x²+y²z) i+(x²+xy²) j+(x²+z²) k, and C is…

A:

Q: Let S be the surface given by x² + y²+2z² = 1, x > 0, y ≥ 0, z ≥ 0. Find the flux of (z, 0, 0)…

A: Step 1:The surface S given by x2+y2+2z2=1 is an ellipsoid, and we are considering the upper half…

Q: 2. Consider the surface defined by Let F(x, y, z) = cos(x) + е¹² + yz. (a) Evaluate F(0,1,2). xz…

A:

Q: Evaluate the surface integral [[ (a² + y²) dS where S is the surface with vector function r(u, v) =…

A:

Q: (x², y², z(x² + y²)) around any closed curve on the surface of Show that the circulation of F = the…

A: Circulation of vector field F around a close curve C = ∫CF.ds If parametric equation of curve C…

Q: (1) Let F(r, y, z) = (y², e², z). (a) Compute the divergence of F. (b) Use the divergence theorem to…

A: Answer

Q: x² - y²-2²-4x - 2z+3=0

A: The given surface is x2-y2-z2-4x-2z+3=0T is the trace of S using x=2.To find the two cordinate when…

Q: • SS,F. F = (4x³z, 4y³z, 3z¹) Calculate F.ds where and S is the surface of the solid bounded by the…

A: Given,                           F→=4x3z, 4y3z, 3z4, and S is the surface of the solid bounded by…

Q: Exercise 5. Compute F F.NdS where F(x, y, z) surface of the plane x + 2y + z = 6 in the first…

A:

Q: Give a parameterization for the surface z F(u, v) = (u, v, ). x² - y²: = x

A: NOTE: Refresh your page if you can't see any equations. . the given surface is

Q: Let S be the quadratic surface given by S = {(x, y, z) | z = 4x² - y², z ≥ 0}, oriented with the…

A:

Q: i) Find g1 (0, 4). ii) Find g2 (0, 4). iii) Find the equation of the tangent plane to the surface z…

A: Since g(x, y) = f(3cosxy,y+exy)

Q: The tangent plane and the normal line of the surface x = y? + z2 + l at (3, 1, -1) have the…

A: Solve the following

Q: Let z = g(x, y) = f(3 cos(ry), y + e) provided that f(3, 7) = 4, fi(3, 7) = 2, f2(3, 7) i) Find g1…

A: