Evaluate the surface integral [/ where F(x, y, z)= xi + yj + z²k and S is the surface parameterized by Φ (u, v) = (2 sin u, 3 cos u, v) with 0 ≤ u ≤ 2л and 0 ≤ v ≤ 1. F.dS,

Q: Let z g(x, y) = f(3 cos(xy), y + e#v) provided that f(3,5) = 4, f1(3, 5) = 2, f2(3, 5) = 4. i) Find…

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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)…

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

A: Let z=gx,y=f3cosxy, y+exy f3,7=4, f13,7=2, f23,7=3

Q: Let z = g(x, y) = f(3 cos(ry), y+ e") provided that f(3, 5) = 5, fi(3, 5) = 2, f2(3, 5) = 4. %3D %3D…

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Q: Compute the surface area of the surface segment parametrised by x(u, v) = u² cos v, y(u, v) = u² sin…

A: Given, xu,v=u2cosv,yu,v=u2sinv,zu,v=u2where 1≤u≤3 and 0≤v≤2π To find the surface area.

Q: Evaluate . F dr where F(x,y,z) = (cos x, -2x, y + sin(z³)) and C is the boundary of the triangle…

A: This is a problem of surface integral.

Q: Consider the surface S(u, v) = -dS.

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Q: Calculate F . dS where F = (4x°z, 4y°z, 3z*) S is the surface of the solid bounded by the…

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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)…

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Q: 1 − v2), 0 ≤ u ≤ 2π, v ≥ 0.

A: The surface S is a portion of a paraboloid that opens downwards, truncated at its base. To see this,…

Q: Let z = g(x, y) = f(3 cos(xy), y + ev) provided that f(3,6)= 7, f₁(3,6) = 2, f₂(3,6)= 5. i) Find g₁…

A: note :Since you have posted multiple questions, we will provide the solution only to the first…

Q: Let z = g(x, y) = f(3 cos(ry), y + e²") provided that f(3,5) = 7, f1(3,5) = 2, f2(3, 5) = 5. i) Find…

A: The function given z=gx,y=f3cosxy,y+exy;f3,5=7,f13,5=2,f23,5=5. i. Find g10,4

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…

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Q: Find g, (0,3). ) Find g2 (0, 3). i) Find the equation of the tangent plane to the surface z = f(3…

A: 1st option is correct

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…

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

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Q: Set up and evaluate the surface integral ||(4x+z+6)dS over the surface S ř (u,v)=(v, 4cos u, 4sin u)…

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Q: Let f(x,y,z)=-x^2+sin(y)-2z^2=0 define a surface in 3 dimensions. Find the equation of the normal…

A: Given the surface fx,y,z=-x2+siny-2z2=0. Let us find the equation of the normal to the surface in…

Q: Evaluate f(V x F) dS where S is the surface x² + y² +3z² = 1, z ≤0 and F = (y, -x, zx³y²). Let the…

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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)