Evaluate the surface integral f(x,y,z) ds using a parametric description of the surface. S 2 2 2 f(x,y,z) = 3x² + 3y², where S is the hemisphere x² + y² + z² =25, for zz0 Write a parametric description of the given hemisphere using up and v=0. r(u,v) = where 0 sus and s (Type exact answers.) SVS

Q: Sketch the graph of the parametric equations x = sint, y = 2 cos(3t), π ≤ t ≤ 27. Clearly label the…

A: We are to sketch the graph of the parametric equationsx = sint, y = 2 cos(3t), π < t < 2π.…

Q: Answer the question below: The student should identify the cartesian equation of a given plane that…

A: Let's find.

Q: Consider the surface S parametrized by R(u, v) (uv, sin u, cos v). Find an equation for the tangent…

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Q: 2. Consider the surface defined by 1² + 2xy + y² + 2²-25 Let F(x, y, z)-1² + 2xy + y² + 2². (a)…

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Q: Given the surface z = In(-2x² + 5y² – xy). Find the directional derivative of the function f at…

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Q: Don't use chat gpt It Chatgpt means downvote

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Q: 2. Consider the two surfaces zx = x² + y? and z³ = 4(x² + y³) They have a curve of intersection C…

A: a) The two surfaces are zx=x2+y2 and z3=4x2+y2. To find the curve of intersection of these two…

Q: Let S be the parametric surface, parameterized by r(u, v) = e" cos vi + e" sin vj + uk, (u,v) E D =…

A: given S be the parametric surface, parametrized by  ru,v=eu cosv i^+eu sinv j^+u k^  here…

Q: valuate V x F . dS, 4 S here F(x, y, z) = (zy, x²y²z², –yx) and S is the surface of the phere x2 +…

A: Stokes theorem is used

Q: Consider the surface r²+y²+2ry-3x+2y-2z=1. Determine the following: (a) the general equation of the…

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Q: Find a parametric representation of the surface in terms of parameters u = x and v = y. NOTE: Enter…

A: a) z+zx2-6y=0b) y2-10z=11

Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

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Q: 2. -) Consider the surface x² + y²-2xy-x+3y-z=-4 at the point Po(2, -3, 18). Determine the…

A: Let's find equation of tangent plane and parametric equations of normal line.

Q: Let S be the parametric surface: r(u, v) = (u2, u cos v, u sin v). Find the tangent plane equation…

A: The given problem is to find the tangent plane equation for the given parametric surface at given…

Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,n2, n3),B(m,m2,m,),C(r..). 2.…

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Q: (a) (b) (c) r(u, v) = (u cos v, u sin v, v); u € [0, 2], v € [0, π]. (*) Find r, and r. (**)…

A: Surface integral of a function f(x,y,z) on a parametric surface r(u,v) in the region D  ∫∫Dfx(u,v) ,…

Q: Calculate Tu, T₁, and n(u, v) for the parametrized surface at the given point. Then find the…

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Q: Match the parametrizations to the surfaces shown in the figures. Þ(u, v) = v 4² u cos(v) (u, U) = |…

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Q: ) Consider the surface x² + y²-2xy-x+3y-z=-4 at the point Po(2, -3, 18). Determine the following:…

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Q: Calculate Tu, T₁, and n(u, v) for the parametrized surface at the given point. Then find the…

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Q: Find parametric equations for the surface obtained by rotating the curve y = eX, 0 sx 5 4, about the…

A: Consider the curve y=e-x,    0≤x≤4 Recollect: The parametric equations of the surface obtained by…

Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

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Q: If a parametric surface given by r1(u, v) = f(u, v)i + g(u, v)j+ h(u,v)k and –1< u<1, –2 < v< 2, has…

A: We will find out the required value.