Compute the differential of surface area for the surface S described by the given parametrization. (u, v) = (eu cos(v), eª sin(v), uv), D = {(u, v) | 0 ≤ u ≤ 4, 0 ≤ v ≤ 2π} 1) dS = dA

Q: Find the parametric equations of normal line to the surface given by f(x,y) = tan Vx2 + y² at the…

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Q: find the tangent plane to the surface z = Vy-x at the point (1,2,1)

A: Equation of tangent plane is z-c = df/dx(x-a)+df/dy(y-b) at point (a,b,c)

Q: Consider the surface xyz = 20. A. Find the unit normal vector to the surface at the point (5, 2, 2)…

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Q: x² + y³. 2 = Consider the surface S of equation (1, 1, v), An equation for the tangent line tangent…

A: We have to find the equation of tangent line.

Q: Find an equation of the tangent plane to the given surface at the specified point z = sin(xy), (x,v)…

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Q: A surface z = f(x, y) is defined implicitly by the equation x +y+ z – e² = 3 – e. - Determine the…

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Q: Q2: A. For the surface f derivative at (1,1 derivative and the line to the surface

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Q: b) Find equations for the tangent plane and normal line at the point po on the given surface.…

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Q: 1. Consider the ellipsoid (a) Parametrize the surface S = r(u,v) by z = a sin(u) sin(v), y = bcos(u)…

A: Using the parameters on the equation of ellipsoid:…

Q: Consider the following surface parametrization. x = 3 cos(0) sin(4), y = 2 sin(0) sin(4), cos(4)…

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Q: Suppose A is the vector field A = xi. Calculate A ·î dS using the projection theorem. [You may…

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Q: Solve the initial value problem (1+ 2?)y" + 3y = 0, y(0) = 0, y'(0) = 8. %3D If the solution is y =…

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Q: 3. What is the tangent plane to the surface 4x4 2xy + 7xyz -5 at the point P(1, 1, -1)? Find the…

A: Given plane 4x4-2xy+7xyz=-5 and point P1,1,-1 Let Fx,y,z=4x4-2xy+7xyz+5